111 results on '"Uniformly stable"'
Search Results
2. A Uniformly Robust Staggered DG Method for the Unsteady Darcy-Forchheimer-Brinkman Problem
- Author
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Zhao, Lina, Lam, Ming Fai, and Chung, Eric
- Published
- 2022
- Full Text
- View/download PDF
3. Uniformly stable and attractive of fractional-order memristor-based neural networks with multiple delays.
- Author
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Yao, Xueqi, Zhong, Shouming, Hu, Taotao, Cheng, Hong, and Zhang, Dian
- Subjects
- *
FRACTIONAL calculus , *MEMRISTORS , *ARTIFICIAL neural networks , *TIME delay systems , *LINEAR systems - Abstract
Abstract Memristive neural networks (MNN) have been wildly studied. Nevertheless, fractional -order memristive neural networks (FMNN) still remain a wide-open dilemma. This paper addresses the problem of FMNN systems with multiple delays and grew several related theories through the study. First, the existence of the system equilibrium point is investigated based on contraction mapping principle, and a new sufficient criterion is obtained. Second, the delay-free uniform stability of the system is discussed by employing differential inclusion theory. Third, a novel asymptotic stability criterion is proposed which is less conservative. Finally, one descriptive numerical example and simulation results emphasize the accuracy and reliability of the proposed results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
4. A UNIFORMLY STABLE SOLVABILITY OF NLBVP FOR PARAMETERIZED ODE
- Author
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Dovlet Dovletov
- Subjects
Uniformly stable ,Computer Science, Interdisciplinary Application ,Differential equation ,differential equation,nonlocal boundary problem,a uniform solvability ,General Chemical Engineering ,Ode ,Parameterized complexity ,Applied mathematics ,Bilgisayar Bilimleri, Disiplinler Arası Uygulamalar ,Mathematics - Abstract
Nonlocal boundary value problem of the first kind for an odinary linear second order differential equation with positive parameter at the highest derivative is considered. The existence and uniqueness, as well as, a uniformly stable estimate of classical solution is established under accurate condition on coefficients and location of nonlocal data carriers of multipoint boundary value condition. An essentiality of the revealed condition is confirmed by ill-posed problem examples.
- Published
- 2021
5. Uniform stability for the 3D magneto-hydrodynamics equations
- Author
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Fan Wu
- Subjects
Physics::Fluid Dynamics ,Physics ,Forcing (recursion theory) ,Uniformly stable ,Mathematics::Quantum Algebra ,Weak solution ,Mathematics::Analysis of PDEs ,General Physics and Astronomy ,Perturbation (astronomy) ,Mechanics ,Magnetohydrodynamics ,Stability (probability) ,Mathematical Physics - Abstract
In this note, we are concerned with uniform stability for a Leray–Hopf weak solution of the MHD equations and obtain that the Leray–Hopf weak solution is uniformly stable with respect to a small perturbation of initial velocity, magnetic and external forcing. This extends and improves the results given by Gallagher–Planchon and Dong–Jia for Navier–Stokes equations.
- Published
- 2021
6. Asymptotic stability of fractional resolvent families
- Author
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Miao Li and Chen-Yu Li
- Subjects
Mathematics::Functional Analysis ,Uniformly stable ,Generator (category theory) ,010102 general mathematics ,Banach space ,01 natural sciences ,Abelian and tauberian theorems ,010101 applied mathematics ,Combinatorics ,Mathematics (miscellaneous) ,Exponential stability ,Bounded function ,0101 mathematics ,Mathematics ,Resolvent - Abstract
In this paper, we investigate the asymptotic stability of fractional resolvent families on Banach spaces and ordered Banach spaces. We show that an $$\alpha $$ -times resolvent family $$S_\alpha (t)$$ with generator A is uniformly Abel-stable if and only if $$0\in \rho (A)$$ , and if in addition $$S_\alpha (t)$$ is analytic and bounded, then $$S_\alpha (t)$$ is uniformly stable with $$\Vert S_\alpha (t)\Vert = O(t^{-\alpha })\, (t \rightarrow \infty )$$ . For a bounded positive $$\alpha $$ -times resolvent family on an ordered Banach space, we show that it cannot be uniformly stable if $$\alpha \in (1,2)$$ ; in the case of $$\alpha \in (0,1)$$ , $$0 \in \rho (A)$$ implies the same decay rate $$t^{-\alpha }$$ . Several results on strong stability are also given by using contour integrals, Tauberian theorems and subordination principles.
- Published
- 2021
7. Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations
- Author
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Peng Zhu, Shangyou Zhang, and Fuzheng Gao
- Subjects
Numerical Analysis ,Uniformly stable ,Applied Mathematics ,Mathematical analysis ,010103 numerical & computational mathematics ,01 natural sciences ,Finite element method ,010101 applied mathematics ,Computational Mathematics ,Norm (mathematics) ,Boundary value problem ,0101 mathematics ,Galerkin method ,Convection dominated ,Mathematics - Abstract
In this paper, a modified weak Galerkin (MWG) finite element method with weakly imposed boundary conditions is presented for solving convection-dominated diffusion equations. The method is shown uniformly stable for all diffusion parameters. The method converges at the optimal order for large diffusion problems in the energy norm, and at half a super-convergent order for small diffusion problems. Various numerical examples are presented, showing that the method is as effective as the weak Galerkin method.
- Published
- 2020
8. Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
- Author
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Rob Stevenson, Jan Westerdiep, and Analysis (KDV, FNWI)
- Subjects
Partial differential equation ,Discretization ,Uniformly stable ,Applied Mathematics ,General Mathematics ,Space time ,Numerical Analysis (math.NA) ,Stability (probability) ,Finite element method ,Computational Mathematics ,35K20, 41A25, 65M12, 65M15, 65M60 ,FOS: Mathematics ,Applied mathematics ,Mathematics - Numerical Analysis ,Galerkin method ,Mathematics - Abstract
We analyze Galerkin discretizations of a new well-posed mixed space–time variational formulation of parabolic partial differential equations. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The method is compared to two related space–time discretization methods introduced by Andreev (2013, Stability of sparse space-time finite element discretizations of linear parabolic evolution equations. IMA J. Numer. Anal., 33, 242–260) and by Steinbach (2015, Space-time finite element methods for parabolic problems. Comput. Methods Appl. Math., 15, 551–566).
- Published
- 2020
9. Stability of Numerical Methods for Solving Second-Order Hyperbolic Equations with a Small Parameter
- Author
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Alexander Zlotnik and Boris N. Chetverushkin
- Subjects
Discretization ,Uniformly stable ,General Mathematics ,Numerical analysis ,010102 general mathematics ,Mathematical analysis ,Perturbation (astronomy) ,01 natural sciences ,Finite element method ,010305 fluids & plasmas ,0103 physical sciences ,Time derivative ,0101 mathematics ,Hyperbolic partial differential equation ,Mathematics - Abstract
We study a symmetric three-level (in time) method with a weight and a symmetric vector two-level method for solving the initial-boundary value problem for a second-order hyperbolic equation with a small parameter $$\tau > 0$$ multiplying the highest time derivative, where the hyperbolic equation is a perturbation of the corresponding parabolic equation. It is proved that the solutions are uniformly stable in $$\tau $$ and time in two norms with respect to the initial data and the right-hand side of the equation. Additionally, the case where $$\tau $$ also multiplies the elliptic part of the equation is covered. The spacial discretization can be performed using the finite-difference or finite element method.
- Published
- 2020
10. Noise Stability of Weighted Majority
- Author
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Yuval Peres
- Subjects
Discrete mathematics ,Uniformly stable ,010102 general mathematics ,01 natural sciences ,Noise (electronics) ,Upper and lower bounds ,Combinatorics ,0103 physical sciences ,Exponent ,Noise stability ,Noise sensitivity ,010307 mathematical physics ,0101 mathematics ,Boolean function ,Mathematics - Abstract
Benjamini et al. (Inst Hautes Etudes Sci Publ Math 90:5–43, 2001) showed that weighted majority functions of n independent unbiased bits are uniformly stable under noise: when each bit is flipped with probability 𝜖, the probability p𝜖 that the weighted majority changes is at most C𝜖1∕4. They asked what is the best possible exponent that could replace 1∕4. We prove that the answer is 1∕2. The upper bound obtained for p𝜖 is within a factor of \(\sqrt {\pi /2}+o(1)\) from the known lower bound when 𝜖 → 0 and n𝜖 →∞.
- Published
- 2020
11. Human thermal responses to temperature ramps in moderate built environments
- Author
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Shuai Zhang and Neng Zhu
- Subjects
medicine.medical_specialty ,High energy ,Environmental Engineering ,Uniformly stable ,Geography, Planning and Development ,Humidity ,Thermal comfort ,Building and Construction ,Thermal sensation ,Audiology ,Sensation ,Thermal ,medicine ,Environmental science ,Cooling energy ,Civil and Structural Engineering - Abstract
Current studies demonstrate that uniformly stable indoor thermal environments do not completely ensure the thermal comfort of residents, and unreasonable temperature settings can cause discomfort and high energy consumption. Moreover, temperature ramps frequently occur in actual indoor environments. Thus, it is important to understand human thermal responses in moderate environments with temperature ramps to improve working conditions and reduce energy consumption. In this regard, an experiment using within−subjects design in a chamber was conducted to evaluate the effects of temperature ramps on human thermal responses. A total of 60 healthy participants (30 females and 30 males) were recruited to participate in the tests. Their subjective responses, thermal comfort and sensation, thermal acceptability and preference, humidity perception and facial thermal sensation were collected during the experiments. The results showed that temperature ramps significantly affected the thermal sensation, thermal comfort, and facial sensation in the ramp-down environments but not significantly in ramp-up environments. However, the effect of temperature ramp-down on the humidity sensation was only significant for the female participants. A 2 °C temperature ramp-up did not affect the thermal comfort of the participants and was acceptable for them. The male participants were more receptive to ambient temperatures than the female ones, whereas the female participants were more sensitive to cool environments than the male ones. Moreover, good fitting relationships between the thermal sensation and the thermal comfort, as well as the thermal sensation and the facial thermal sensation were observed. This study provides some references for the influence of temperature ramps on human thermal responses in actual indoor environments, and recommends temperature set points to reduce the use of cooling energy.
- Published
- 2022
12. Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems
- Author
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Bin Zhou and Weiwei Luo
- Subjects
0209 industrial biotechnology ,Uniformly stable ,Dynamical Systems (math.DS) ,02 engineering and technology ,Stability (probability) ,Moment (mathematics) ,020901 industrial engineering & automation ,Exponential stability ,Control and Systems Engineering ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Mathematics - Dynamical Systems ,Electrical and Electronic Engineering ,Markovian switching ,Mathematics - Abstract
The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability theorems. Both p-th moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison principles. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results.
- Published
- 2018
13. A Different Shade of Gray: Midlife and Beyond in the Inner City
- Author
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Hui-Peng Liew
- Subjects
050402 sociology ,Uniformly stable ,05 social sciences ,0506 political science ,0504 sociology ,Inner city ,Aesthetics ,Premise ,050602 political science & public administration ,Sociology ,Life-span and Life-course Studies ,Older people ,Gerontology ,Gray (horse) ,Demography - Abstract
In this well-researched book, Katherine Newman challenges the notion that the living environments of older people are uniformly stable and desirable. The premise of this book is that the life pathw...
- Published
- 2018
14. Asymptotic preconditioning of linear homogeneous systems of differential equations
- Author
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Trench, William F.
- Subjects
- *
ASYMPTOTIC theory in linear differential equations , *NUMERICAL solutions to linear differential equations , *MATHEMATICAL analysis , *EQUILIBRIUM , *STABILITY (Mechanics) , *LINEAR systems - Abstract
Abstract: We consider the asymptotic behavior of solutions of a linear differential system , where A is continuous on an interval . We are interested in the situation where the system may not have a desirable asymptotic property such as stability, strict stability, uniform stability, or linear asymptotic equilibrium, but its solutions can be written as , where P is continuously differentiable on and u is a solution of a system that has the property in question. In this case we say that P preconditions the given system for the property in question. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
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15. Differentiability of solutions to second-order elliptic equations via dynamical systems
- Author
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Maz'ya, Vladimir and McOwen, Robert
- Subjects
- *
NUMERICAL solutions to elliptic differential equations , *LIPSCHITZ spaces , *CONTINUITY , *ASYMPTOTIC expansions , *DYNAMICS , *MATHEMATICAL analysis - Abstract
Abstract: For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of continuity satisfying the square-Dini condition, and obtain additional conditions that examples show are sharp. Our results extend those of previous authors who assume the modulus of continuity satisfies the Dini condition. Our method involves the study of asymptotic properties of solutions to a dynamical system that is derived from the coefficients of the elliptic equation. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
16. LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT METHODS FOR DARCY-STOKES PROBLEMS.
- Author
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Shiquan Zhang, Xiaoping Xie, and Yumei Chen
- Subjects
- *
FINITE element method , *STOKES equations , *POISSON'S equation , *PERTURBATION theory , *MATHEMATICS - Abstract
In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2009
17. UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS.
- Author
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Xiaoping Xie, Jinchao Xu, and Guangri Xue
- Subjects
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DARCY'S law , *STOKES equations , *FINITE element method , *PARTIAL differential equations , *MATHEMATICS - Abstract
In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that tremors both Darcy's law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zeroth-order term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods are based on the original weak formulations of Darcy-Stokes-Brinkman equations. In the first method we consider the existing Stokes elements. We show that a stable Stokes element is also uniformly stable with respect to the coefficients and the jumps of Darcy-Stokes-Brinkman equations if and only if the discretely divergence-free velocity implies almost everywhere divergence-free one. In the second method we construct uniformly stable elements by modifying some well-known H(div)-conforming elements. We give some new 2D and 3D elements in a unified way. In the last method we modify the original weak formulation of Darcy-Stokes-Brinkman equations with a stabilization term. We show that all traditional stable Stokes elements are uniformly stable with respect to the coefficients and their jumps under this new formulation. [ABSTRACT FROM AUTHOR]
- Published
- 2008
18. Stability in m-dimensional linear delay difference system.
- Author
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Tang, X. H. and Zhiyuan Jiang
- Subjects
- *
DIFFERENCE equations , *STABILITY (Mechanics) , *VECTOR analysis , *EIGENVALUES , *MATRICES (Mathematics) , *DIFFERENCE algebra - Abstract
In this paper, we give some sufficient conditions for the zero solution of an m-dimensional delay difference equation of the form[image omitted] to be uniformly stable and asymptotically stable. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
19. Uniformly stable wavelets on nonuniform triangulations
- Author
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Tom Lyche, Solveig Bruvoll, and Knut Mrken
- Subjects
Numerical Analysis ,General Computer Science ,Uniformly stable ,Applied Mathematics ,020207 software engineering ,02 engineering and technology ,Computer Science::Computational Geometry ,01 natural sciences ,0104 chemical sciences ,Theoretical Computer Science ,Piecewise linear function ,Combinatorics ,010404 medicinal & biomolecular chemistry ,Wavelet ,Modeling and Simulation ,Norm (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,MathematicsofComputing_DISCRETEMATHEMATICS ,ComputingMethodologies_COMPUTERGRAPHICS ,Mathematics - Abstract
In this paper we construct linear, uniformly stable, wavelet-like functions on arbitrary triangulations. As opposed to standard wavelets, only local orthogonality is required for the wavelet-like functions. Nested triangulations are obtained through refinement by two standard strategies, in which no regularity is required. One strategy inserts a new node at an arbitrary position inside a triangle and then splits the triangle into three smaller triangles. The other strategy splits two neighbouring triangles into four smaller triangles by inserting a new node somewhere on the edge between the triangles. In other words, non-uniform refinement is allowed in both strategies. The refinement results in nested spaces of piecewise linear functions. The detail-, or wavelet-spaces, are made to satisfy certain orthogonality conditions which locally correspond to vanishing linear moments. It turns out that this construction is uniformly stable in the L norm, independently of the geometry of the original triangulation and the refinements.
- Published
- 2017
20. A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations
- Author
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Peiqi Huang and Zhilin Li
- Subjects
Coupling ,Control and Optimization ,Darcy's law ,Uniformly stable ,Matching (graph theory) ,Interface (Java) ,Applied Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Finite element method ,010101 applied mathematics ,Computational Mathematics ,Consistency (statistics) ,Modeling and Simulation ,Fluid–structure interaction ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
A nonconforming rectangular finite element method is proposed to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures. A uniformly stable mixed finite element together with Nitsche-type matching conditions that automatically adapt to the coupling of different sub-problem combinations are utilized in the discrete algorithm. Compared with other finite element methods in the literature, the new method has some distinguished advantages and features. The Boland-Nicolaides trick is used in proving the inf-sup condition for the multidomain discrete problem. Optimal error estimates are derived for the coupled problem by analyzing the approximation errors and the consistency errors. Numerical examples are also provided to confirm the theoretical results.
- Published
- 2017
21. Stability in <f>n</f>-dimensional delay differential equations
- Author
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Tang, X.H.
- Subjects
- *
DIFFERENTIAL equations , *BESSEL functions , *CALCULUS , *LITERATURE - Abstract
In this paper, we give some sufficient conditions for the zero solution of an
n -dimensional delay differential equation of the form to be uniformly stable and asymptotically stable. These conditions extend and improve the existing relative results in literature. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
22. Stability of a periodic solution for fuzzy differential equations.
- Author
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Jeong, Jae
- Abstract
In this paper, we consider the fuzzy differential equations where F(t,x(t)) is a continuous fuzzy mapping on [0, ∞)× E
n . The purpose of this paper is to prove that the solution ϕ( t) of the fuzzy differential equations is equiasymptotically stable in the large and uniformly asymptotically stable in the large. [ABSTRACT FROM AUTHOR]- Published
- 2003
- Full Text
- View/download PDF
23. H∞ model reduction of switched LPV systems via semi-time-varying reduced-order model
- Author
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Wei Xing Zheng, Lixian Zhang, and Huijun Gao
- Subjects
0209 industrial biotechnology ,Engineering ,General Computer Science ,Uniformly stable ,business.industry ,Mechanical Engineering ,Parameterized complexity ,02 engineering and technology ,Sense (electronics) ,Reduced order ,Reduction (complexity) ,020901 industrial engineering & automation ,Computer Science::Systems and Control ,Control and Systems Engineering ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,Errors-in-variables models ,020201 artificial intelligence & image processing ,Electrical and Electronic Engineering ,business - Abstract
This paper investigates the problem of model reduction for a class of switched linear parameter varying (LPV) systems with persistent dwell-time (PDT) switching property. The PDT switching generalizes the dwell-time and average dwell-time switching that are commonly concerned in the existing literature. To reduce the original high-order model with less conservatism, the constructed reduced-order model is both parameterized and semi-time-varying such that the model error system is uniformly stable over the PDT switching and guarantees an error performance in H ∞ sense. A numerical example is used to verify the validity and advantage of the theoretical results.
- Published
- 2016
24. A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations
- Author
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Lin Zhu
- Subjects
Multidisciplinary ,General Computer Science ,Uniformly stable ,Discretization ,Article Subject ,Order (ring theory) ,010103 numerical & computational mathematics ,01 natural sciences ,Stability (probability) ,lcsh:QA75.5-76.95 ,Fractional calculus ,010101 applied mathematics ,Operator (computer programming) ,Scheme (mathematics) ,Fractional diffusion ,Applied mathematics ,lcsh:Electronic computers. Computer science ,0101 mathematics ,Mathematics - Abstract
Using the asymmetric discretization technique, an explicit finite difference scheme is constructed for one-dimensional spatial fractional diffusion equations (FDEs). The spatial fractional derivative is approximated by the weighted and shifted Grünwald difference operator. The scheme can be solved explicitly by calculating unknowns in the different nodal-point sequences at the odd time-step and the even time-step. The uniform stability is proven and the error between the discrete solution and analytical solution is theoretically estimated. Numerical examples are given to verify theoretical analysis.
- Published
- 2019
25. Razumikhin and Krasovskii stability theorems for time-varying time-delay systems
- Author
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Bin Zhou and Alexey V. Egorov
- Subjects
0209 industrial biotechnology ,Uniformly stable ,Mathematical analysis ,Negativity effect ,02 engineering and technology ,Type (model theory) ,Stability (probability) ,Constructive ,Stability conditions ,020901 industrial engineering & automation ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Electrical and Electronic Engineering ,Mathematics - Abstract
The main results of the paper are generalizations of the Razumikhin and of the Krasovskii classical stability theorems for stability analysis of time-varying time-delay systems. The condition of negativity of the time-derivative of Razumikhin functions and Krasovskii functionals is weakened. This is achieved by using the notion and properties of uniformly stable functions. We also show how to apply the results to the stability analysis of linear time-varying time-delay systems of retarded type. Both the system matrices and time-delays are allowed to be time-varying. Some constructive sufficient stability conditions are obtained and their effectiveness is demonstrated by some examples.
- Published
- 2016
26. On the Residual Uniform Stability of Linear Systems with Unbounded Coefficients
- Author
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N. L. Margolina
- Subjects
Statistics and Probability ,Dimension (vector space) ,Exponential stability ,Uniformly stable ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Linear system ,Residual ,Stability (probability) ,Mathematics - Abstract
It is shown that there exist linear nonautonomous systems of any dimension that have unbounded coefficients and possess the properties of residual uniform stability and asymptotic stability, but are not uniformly stable.
- Published
- 2015
27. Uniformly Stable Explicitly Solvable Finite Difference Method for Fractional Diffusion Equations
- Author
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Hongxing Rui and Jian Huang
- Subjects
Cardinal point ,Uniformly stable ,Discretization ,Control theory ,Applied Mathematics ,Scheme (mathematics) ,Finite difference method ,Applied mathematics ,Differential (infinitesimal) ,Space (mathematics) ,Mathematics ,Fractional calculus - Abstract
A finite difference scheme for the one-dimensional space fractional diffusion equation is presented and analysed. The scheme is constructed by modifying the shifted Grünwald approximation to the spatial fractional derivative and using an asymmetric discretisation technique. By calculating the unknowns in differential nodal point sequences at the odd and even time levels, the discrete solution of the scheme can be obtained explicitly. We prove that the scheme is uniformly stable. The error between the discrete solution and the analytical solution in the discretel2norm is optimal in some cases. Numerical results for several examples are consistent with the theoretical analysis.
- Published
- 2015
28. Extension of NXFEM to nonconforming finite elements
- Author
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Didier Graebling, H. El-Otmany, Daniela Capatina, R. Luce, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Institut des sciences analytiques et de physico-chimie pour l'environnement et les materiaux (IPREM), and Université de Pau et des Pays de l'Adour (UPPA)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
General Computer Science ,Uniformly stable ,Finite element approximations ,Basis function ,010103 numerical & computational mathematics ,01 natural sciences ,Theoretical Computer Science ,Mathematics::Numerical Analysis ,Robustness (computer science) ,Applied mathematics ,[CHIM]Chemical Sciences ,NXFEM ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] ,0101 mathematics ,Robustness ,Mathematics ,Extended finite element method ,Discrete mathematics ,Numerical Analysis ,Applied Mathematics ,Interface ,Finite element method ,010101 applied mathematics ,Nonconforming finite elements ,Modeling and Simulation ,Stokes problem ,A priori and a posteriori ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
International audience; In this paper, we consider triangular nonconforming finite element approximations of an interface elliptic problem. We propose two extensions of the conforming Nitsche's extended finite element method to the nonconforming case. The first one is obtained by adding stabilisation terms on the cut edges, and the second one by modifying the Crouzeix-Raviart basis functions on the cut cells. Both discrete problems are uniformly stable and yield optimal a priori error estimates, uniformly with respect to the diffusion parameters. Moreover, we show that they exhibit the same robustness with respect to the position of the interface as the classical conforming method. We then validate these results numerically. Finally, we propose a nonconforming approximation of the interface Stokes problem based on the modified Crouzeix-Raviart elements and we illustrate it numerically. c; Dans cet article, nous considérons les approximations par éléments finis triangulaires non conformes d'un problème elliptique d'interface. Nous proposons deux extensions de la méthode d'éléments finis étendue de Nitsche conforme au cas non conforme. La première est obtenue en ajoutant des termes de stabilisation sur les bords coupés, et la seconde en modifiant les fonctions de base de Crouzeix-Raviart sur les cellules coupées. Les deux problèmes discrets sont uniformément stables et donnent des estimations d'erreur a priori optimales, uniformément par rapport aux paramètres de diffusion. De plus, nous montrons qu'ils présentent la même robustesse vis-à-vis de la position de l'interface que la méthode classique de conformation. Nous validons ensuite ces résultats numériquement. Enfin, nous proposons une approximation non-conforme du problème de Stokes de l'interface basée sur les éléments de Crouzeix-Raviart modifiés et nous l'illustrons numériquement.
- Published
- 2017
29. Lyapunov density for coupled systems
- Author
-
Umesh Vaidya and Rajeev Rajaram
- Subjects
Lyapunov function ,Equilibrium point ,Uniformly stable ,Advection ,Applied Mathematics ,Mathematical analysis ,Probability density function ,Stability (probability) ,symbols.namesake ,Ordinary differential equation ,symbols ,Almost everywhere ,Analysis ,Mathematics - Abstract
We prove a necessary and sufficient condition for the existence of Lyapunov density for a system of coupled autonomous ordinary differential equations. In particular, we characterize the kinds of couplings that preserve almost everywhere uniform stability of the origin provided the isolated systems have an almost everywhere uniformly stable equilibrium point at the origin.
- Published
- 2014
30. Stability of a family of difference schemes for the Samarskii-Ionkin problem with variable coefficient
- Author
-
A. Yu. Mokin
- Subjects
Variable coefficient ,Partial differential equation ,Uniformly stable ,General Mathematics ,Norm (mathematics) ,Ordinary differential equation ,Mathematical analysis ,Spectral properties ,Grid ,Analysis ,Mathematics - Abstract
We consider a one-parameter family of difference schemes approximating a nonlocal heat problem with variable coefficient. We study the spectral properties of the main difference operator of the scheme. An energy norm in which the schemes are uniformly stable is defined on the space of grid functions. The corresponding stability condition is derived.
- Published
- 2014
31. 3/2 -stability conditions for a class of Volterra–Levin equations
- Author
-
Dianli Zhao and Sanling Yuan
- Subjects
Class (set theory) ,Stability conditions ,Uniformly stable ,Exponential stability ,Applied Mathematics ,Stability theory ,Mathematical analysis ,Zero (complex analysis) ,Applied mathematics ,Analysis ,Marginal stability ,Mathematics - Abstract
In this paper, a generalized Volterra–Levin equation is considered. 3/2-stability conditions are established for ensuring that the zero solution of the equation is uniformly stable, asymptotically stable and globally asymptotically stable. Further results are obtained under nonnegativity assumption. The main results are new and different from the known results.
- Published
- 2014
32. Robust sensorless speed-tracking controller for surface-mount permanent magnet synchronous motors
- Author
-
Ramon Ramirez-Villalobos, Luis N. Coria, Luis T. Aguilar, and Alejandra Ferreira de Loza
- Subjects
0209 industrial biotechnology ,Engineering ,Uniformly stable ,Permanent magnet synchronous motor ,business.industry ,Stator ,020208 electrical & electronic engineering ,Control engineering ,02 engineering and technology ,Mount ,Reduced order ,law.invention ,020901 industrial engineering & automation ,Control theory ,law ,Robustness (computer science) ,0202 electrical engineering, electronic engineering, information engineering ,Torque ,business ,Voltage - Abstract
The sensorless high speed-tracking control problem for a surface-mount permanent magnet synchronous motor via stator currents and voltages measurements is tackled, by interconnecting an H ∞ -controller and a reduced order sliding-mode observer. The observer-control scheme is robust against external load disturbances. The rotor position and speed variables are estimated in finite time by means of a reduced order observer. Thus, an output-feedback H ∞ -controller is designed such that the undisturbed system is uniformly stable around the desired speed reference, whereas the effects of the disturbances are attenuated. The feasibility of the proposed robust sensorless controller is supported by numerical simulations.
- Published
- 2016
33. Uniformly Stable Continuous Solutions Of A Functional Differential Inclusions
- Author
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Fatma M.Gaffar, Nesreen F.M.El-haddad, and Ahmed M. A. El-Sayed
- Subjects
Materials science ,Complementary and alternative medicine ,Differential inclusion ,Uniformly stable ,Mathematical analysis ,Pharmaceutical Science ,Pharmacology (medical) - Published
- 2013
34. Uniformly stable solution of a nonlocal problem of coupled system of differential equations
- Author
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M. El-Gendy, Ahmed M. A. El-Sayed, and R. O. Abd-El-Rahman
- Subjects
Uniformly stable ,System of differential equations ,Organic Chemistry ,Calculus ,Applied mathematics ,Biochemistry ,Stability (probability) ,Mathematics - Abstract
sic) Abstract. In this paper we are concerned with a nonlocal problem of a coupled system of dif- ferential equations. We study the local existence of the solution and its continuous dependence. The global existence and its uniform stability is being studied.
- Published
- 2013
35. Uniformly stable solutions of the functional inclusions
- Author
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Fatma M.Gaffar, Nesreen F.M.El-haddad, and Ahmed M. A. El-Sayed
- Subjects
Materials science ,Uniformly stable ,Chemical physics - Published
- 2012
36. Phase retrieval in infinite-dimensional Hilbert spaces
- Author
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Ingrid Daubechies, Jameson Cahill, and Peter G. Casazza
- Subjects
Pure mathematics ,Uniformly stable ,010102 general mathematics ,Hilbert space ,020206 networking & telecommunications ,02 engineering and technology ,General Medicine ,Contrast (music) ,Stability result ,01 natural sciences ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,symbols.namesake ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,FOS: Mathematics ,0101 mathematics ,Phase retrieval ,Mathematics - Abstract
The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite-dimensional setting in which phase retrieval is always stable. This leads us to derive stability results for signals depending on how well they are approximated by finite expansions.
- Published
- 2016
37. Wave equation with damping affecting only a subset of static Wentzell boundary is uniformly stable
- Author
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Irena Lasiecka, Marcelo M. Cavalcanti, and Daniel Toundykov
- Subjects
Uniformly stable ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Calculus ,Boundary (topology) ,Wave equation ,Mathematics - Abstract
A stabilization/observability estimate and asymptotic energy decay rates are derived for a wave equation with nonlinear damping in a portion of the interior and Wentzell condition on the boundary: ∂ ν u + u = Δ T u \partial _{\nu } u + u = \Delta _{T}u . The dissipation does not affect a full collar of the boundary, thus leaving out a portion subjected to the high-order Wentzell condition. Observability of wave equations with damping supported away from the Neumann boundary is known to be intrinsically more difficult than the corresponding Dirichlet problem because the uniform Lopatinskii condition is not satisfied by such a system. In the case of a Wentzell boundary, the situation is more difficult since the “natural” energy now includes the H 1 H^{1} Sobolev norm of the solution on the boundary. To establish uniform stability it is necessary not only to overcome the presence of the Neumann boundary operator, but also to establish an inverse-type coercivity estimate on the H 1 H^{1} trace norm of the solution. This goal is attained by constructing multipliers based on a refinement of nonradial vector fields employed for “unobserved” Neumann conditions. These multipliers, along with a suitable geometry (local convexity), allow reconstruction of the high-order part of the potential energy from the damping that is supported only in a far-off region of the domain.
- Published
- 2012
38. Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems
- Author
-
Yongke Wu, Li Wang, and Xiaoping Xie
- Subjects
Numerical Analysis ,Singular perturbation ,Uniformly stable ,Applied Mathematics ,Uniform convergence ,Mathematical analysis ,Perturbation (astronomy) ,Finite element method ,Computational Mathematics ,Fourth order ,Norm (mathematics) ,Partial derivative ,Analysis ,Mathematics - Abstract
In this article, we consider rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-C 0 rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a C 0 extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 00: 000–000, 2012
- Published
- 2012
39. Conjugacies between general contractions
- Author
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Claudia Valls and Luis Barreira
- Subjects
Large class ,Numerical Analysis ,Mathematics::Dynamical Systems ,Algebra and Number Theory ,Uniformly stable ,Mathematical analysis ,Exponential contractions ,Exponential function ,Nonlinear system ,Discrete time and continuous time ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,Special case ,Conjugacies ,Mathematics - Abstract
The main aim of this note is to construct topological conjugacies between linear nonautonomous contractions with discrete time. As a consequence, we obtain topological conjugacies between linear and nonlinear nonautonomous contractions. We consider the general case of linear contractions with respect to arbitrary growth rates e - c ρ ( m ) . This includes the usual exponential contractions with ρ ( m ) = m as a very special case. We also consider the case of contractions that are not uniformly stable. In addition, we show that all conjugacies are locally Holder outside the origin, and locally Holder everywhere for a large class of growth rates ρ ( m ) .
- Published
- 2012
- Full Text
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40. Uniformly Stable Positive Monotonic Solution of a Nonlocal Cauchy Problem
- Author
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Kh. W. Elkadeky, E. M. Hamdallah, and Ahmed M. A. El-Sayed
- Subjects
Cauchy problem ,Uniformly stable ,Mathematical analysis ,Monotonic function ,General Medicine ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
In this paper, we study the existence of a uniformly stable positive monotonic solution for the nonlocal Cauchy problem with the nonlocal condition where
- Published
- 2012
41. Stability Behavior of the Zero Solution for Nonlinear Damped Vectorial Second Order Differential Equation
- Author
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Mohamed A. Ramadan and Samah M. Elkholy
- Subjects
Nonlinear system ,Uniformly stable ,Differential equation ,Stability theory ,Mathematical analysis ,Zero (complex analysis) ,Order (ring theory) ,Stability (probability) ,Mathematics - Abstract
In this paper, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of solution of the nonlinear damped vectorial oscillator and the conditions for the stability of the zero solution to be uniformly stable as well as asymptotically stable.
- Published
- 2012
42. Uniform stability of nonautonomous impulsive differential systems with time delay
- Author
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Shukai Duan, Huamin Wang, Chuandong Li, and Lidan Wang
- Subjects
Nonlinear system ,Uniformly stable ,Control theory ,Mathematical proof ,Differential systems ,Stability (probability) ,Mathematics - Abstract
This paper deals with the stability problems of nonautonomous impulsive differential systems with time-delay. By utilizing the method of mathematic induction, proofs by contradiction and Lyapunov-Krasovskii functional, we obtain several uniformly stable criteria about the linear and nonlinear nonautonomous impulsive systems with time delay. One numerical example and its simulations are given to illustrate the effectiveness of the theoretical result.
- Published
- 2015
43. Stability of perturbed -dimensional Volterra differential equations
- Author
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Ruiqi Wang and Xiao Chang
- Subjects
Uniformly stable ,N dimensional ,Differential equation ,Applied Mathematics ,Mathematical analysis ,Zero (complex analysis) ,Integral differential equations ,Stability (probability) ,Analysis ,Mathematics - Abstract
In this work we deal with the problem of the stability and uniform stability of the perturbed n -dimensional Volterra integral and differential equation x ′ ( t ) = A ( t ) x ( t ) + ∫ − ∞ t C ( t , s ) x ( s ) d s + ∫ − ∞ t D ( t , s ) x ′ ( s ) d s + b ( t ) . Some sufficient conditions for the zero solution of this equation to be stable as well as uniformly stable have been obtained.
- Published
- 2011
44. The Boltzmann equation with potential force in the whole space
- Author
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Jie Sun
- Subjects
Cauchy problem ,Steady state ,Uniformly stable ,General Mathematics ,Mathematical analysis ,General Engineering ,Energy method ,Initial value problem ,Convection–diffusion equation ,Space (mathematics) ,Boltzmann equation ,Mathematics - Abstract
In this paper, we consider the Cauchy problem of the Boltzmann equation with potential force in the whole space. When some more natural assumptions compared with those of the previous works are made on the potential force, we can still obtain a unique global solution to the Boltzmann equation even for the hard potential cases by energy method, if the initial data are sufficiently close to the steady state. Moreover, the solution is uniformly stable. Copyright © 2010 John Wiley & Sons, Ltd.
- Published
- 2010
45. Uniformly stable mixedhp-finite elements on multilevel adaptive grids with hanging nodes
- Author
-
Friedhelm Schieweck
- Subjects
Numerical Analysis ,Quadrilateral ,Uniformly stable ,Applied Mathematics ,Geometry ,Topology ,Finite element method ,Mathematics::Numerical Analysis ,Computational Mathematics ,Incompressible flow ,Modeling and Simulation ,Order (group theory) ,Degree of a polynomial ,Hexahedron ,Element (category theory) ,Analysis ,Mathematics - Abstract
We consider a family of quadrilateral or hexahedral mixed hp -finite elements for an incompressible flow problem with Q r -elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
- Published
- 2008
46. Stability inm-dimensional linear delay difference system
- Author
-
Xianhua Tang and Zhiyuan Jiang
- Subjects
Matrix difference equation ,Algebra and Number Theory ,Uniformly stable ,Differential equation ,Applied Mathematics ,Stability theory ,Mathematical analysis ,Zero (complex analysis) ,Finite difference method ,Of the form ,Stability (probability) ,Analysis ,Mathematics - Abstract
In this paper, we give some sufficient conditions for the zero solution of an m-dimensional delay difference equation of the form to be uniformly stable and asymptotically stable.
- Published
- 2007
47. An extended Hu–Washizu formulation for elasticity
- Author
-
B. D. Reddy and J.K. Djoko
- Subjects
Uniformly stable ,Mechanical Engineering ,Computational Mechanics ,General Physics and Astronomy ,Viscoelastic fluid ,Finite element method ,Viscoelasticity ,Computer Science Applications ,Mechanics of Materials ,Incompressible flow ,Calculus ,Compressibility ,Applied mathematics ,Elasticity (economics) ,Mathematics - Abstract
A class of new mixed formulations for elasticity is developed and analysed. The formulations are based on the discrete evss method, introduced in the context of incompressible viscoelastic flows by A. Fortin, M. Fortin and co-workers. A key feature is a stabilization term that renders coercive a problem that might not otherwise be so. The focus in this work is on behaviour in the incompressible limit and the goal is that of obtaining formulations that are uniformly stable and convergent. Concrete examples are presented of element choices that lead to unstable formulations in the classical formulation, and which are stable for the formulations introduced here. A selection of numerical results illustrates in a comparative way the behaviour of the elements introduced.
- Published
- 2006
48. Mapping theorems and Harnack ordering for \rho-contractions
- Author
-
Nicolae Suciu and Gilles Cassier
- Subjects
Discrete mathematics ,Pure mathematics ,Uniformly stable ,General Mathematics ,Mathematics::Analysis of PDEs ,Hilbert space ,symbols.namesake ,Corollary ,Harnack's principle ,Mathematics::Probability ,symbols ,Mathematics ,Harnack's inequality ,Von Neumann architecture - Abstract
We prove here some mapping theorems for the operators of class Cp (p > 0) on Hilbert spaces defined by B. Sz-Nagy and C. Foias in [12]. More precisely, we answer the following question: What can be said about membership of f(T) in the classes Cp (H) when T belongs to a given one of them and f is in the disc algebra? As a corollary, we recover in this way the famous power inequality. We also introduce a Harnack ordering relation between such operators, we define the corresponding Harnack parts in the class Cp, and we give some results related to uniformly stable operators. These parts involve some operatorial Harnack inequalities as well as von Neumann inequalities, which generalize the Harnack inequalities for contractions given by C. Foias [8], K. Fan [5] and I. Suciu [17]. Finally, we define the Harnack and hyperbolic metrics, and we prove that these are complete on the set of all uniformly stable operators, respectively on the Harnack parts of such operators.
- Published
- 2006
49. Convergence in monotone and uniformly stable skew-product semiflows with applications
- Author
-
Xiao-Qiang Zhao and Jifa Jiang
- Subjects
Monotone polygon ,Uniformly stable ,Applied Mathematics ,General Mathematics ,Product (mathematics) ,Convergence (routing) ,Skew ,Applied mathematics ,Mathematics - Published
- 2005
50. A uniformly stable conformal FDTD-method in Cartesian grids
- Author
-
Igor Zagorodnov, Thomas Weiland, and Rolf Schuhmann
- Subjects
Uniformly stable ,Finite-difference time-domain method ,Word error rate ,Conformal map ,Time step ,Computer Science Applications ,law.invention ,law ,Modeling and Simulation ,Convergence (routing) ,Calculus ,Applied mathematics ,Cartesian coordinate system ,Electrical and Electronic Engineering ,Mathematics - Abstract
A conformal finite-difference time-domain algorithm for the solution of electrodynamic problems in general perfectly conducting 3D geometries is presented. Unlike previous conformal approaches it has the second-order convergence without the need to reduce the maximal stable time step of conventional staircase approach. A novel proof for the local error rate for general geometries is given, and the method is verified and compared to other approaches by means of several numerical 2D examples. Copyright © 2003 John Wiley & Sons, Ltd.
- Published
- 2003
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