Search

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric series. With these contiguous relations one can prove several recursion formulas of those series. This theoretical result allows to compute integrals over products of Jacobi polynomials in a very efficient recursive way. Moreover, the authors present an application to numerical analysis where it can be used in algorithms which compute the approximate solution of boundary value problem of partial differential equations by means of the finite elements method. With the aid of the contiguous relations, the approximate solution can be computed much faster than using numerical integration. A numerical example illustrates this effect. [ABSTRACT FROM AUTHOR]

This paper aims to develop an effective theoretical method for analyzing the interaction of interfacial crack and complex defect in functionally graded magnetic-electro-elastic bi-materials with exponential variation under the action of anti-plane incident SH-wave. The boundary value problem of interest is solved by Green's function method. The mechanical model of the cracks is constructed through interface conjunction and crack deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips of the left crack are expressed. The validity of the present method is verified by comparing with a single crack model in previous work. Through the analyses of numerical cases, it can be concluded that the DSIF is related with 3 factors：the geometry of complex defect and crack, the characteristics of incident wave and the inhomogeneity of materials. Comparing with dual integral equations in dealing with asymmetric defects, the method in this paper is relatively more flexible and applicable, also it comes up with a new way to study fracture problems in functionally graded magnetic-electro-elastic materials with more complex defects. [ABSTRACT FROM AUTHOR]

The paper is focused on the numerical analysis of the two-point inverse stationary heat flow problem, namely the identification of the thermal load. Determination of selected parameters is possible on the basis of temperature measurements, done at specified few locations. This problem may be modelled as the optimization problem, standard numerical analysis of which requires multiple solutions of boundary value problems. However, the novel solution approach, proposed here, is based on the well-known concept of the Monte Carlo method with an appropriate random walk technique. It yields explicit stochastic relations combining computed temperatures and all load parameters. Such relations may be directly applied in most standard optimization algorithms, replacing time-consuming solutions of systems of algebraic equations. Moreover, one may construct the semi-analytical approach, in which the unknown load parameters are obtained explicitly, allowing for the elimination of sensitiveness to initial solutions or requirements for admissible load intervals. The paper is illustrated with results of several benchmark problems with simulated measurement data and various numbers of unknown load parameters. The results comparison, between standard element-free methods with selected optimization algorithms as well as the proposed Monte Carlo solution approach is presented and is especially focused on CPU times. [ABSTRACT FROM AUTHOR]

This is a comment on a 2014 paper by Dai and Wang. It is argued that the validation in Dai and Wang's paper is an artifact caused by the boundary conditions of the level-set function, meaning that the effects reported in their paper have little physical relevance. Simulations are presented using Dai and Wang's methods to illustrate this claim. Remarks are made on the choice of boundary conditions for the level-set function, as well as the frequency of reinitialization, both of which are important topics that are sometimes overlooked.Asimple criterion is proposed for determining the appropriate reinitialization frequency in simulations of highly viscous flows. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

This paper presents a spatiotemporal reaction–diffusion model for epidemics to predict how the infection spreads in a given space. The model is based on a system of partial differential equations with the Neumann boundary conditions. First, we study the existence and uniqueness of the solution of the model using the semigroup theory and demonstrate the boundedness of solutions. Further, the proposed model's basic reproduction number is calculated using the eigenvalue problem. Moreover, the dynamic behavior of the disease‐free steady states of the model for R0<1$$ {\mathcal{R}}_0<1 $$ is investigated. The uniform persistence of the model is also discussed. In addition, the global asymptotic stability of the endemic steady state is examined. Finally, the numerical simulations validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the design and analysis of a robust numerical scheme based on an improvised quartic B-spline collocation (IQBSC) method for a class of nonlinear derivative dependent singular boundary value problems (DDSBVP). The convergence analysis of the method is studied by means of Green's function approach. It should be pointed out that the numerical order of convergence of standard quartic B-spline collocation (SQBC) scheme for second-order boundary value problems (BVPs) is four, however, our proposed IQBSC method is shown to be sixth order convergence. To illustrate the applicability and accuracy of the method, we consider eight test problems. The obtained results are compared to those from some existing numerical schemes in order to show the advantage of present method. It is shown that the rate of convergence of present numerical scheme is higher than that of some of existing numerical methods. The CPU time of the present numerical method is provided. [ABSTRACT FROM AUTHOR]

The dynamic fracture of a crack in a functionally graded one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) subjected to a time-harmonic elastic SH-wave is studied by using integral transform technique and Copson method. It is assumed that the crack surface is a partially permeable boundary condition and the material properties vary continuously as an exponential function. With the help of the Fourier transform, the boundary value problem of partial differential equation describing fracture problem is formulated to three pairs of dual integral equations, which are numerically solved by Copson method. Explicit expressions for the electroelastic field including phonon and phason stresses and electric field on the crack face are determined. The dynamic intensity factors of the electroelastic field are obtained in closed form, and some special cases of obtained results are discussed. On the basis of theoretical analysis and numerical simulation of the established models, numerical analysis was then conducted to discuss crack length, gradient parameter, electric boundary condition, electric loading, incident angle, amplitude, and wave number on the fracture characteristics of material. The research of this paper will provide a theoretical basis for nondestructive testing, optimal design, and reliability analysis of materials and will enrich the research content of fracture mechanics of multi-field coupling materials. [ABSTRACT FROM AUTHOR]

In this paper, we transform the given nonlocal boundary condition problem into a manageable local equation. By introducing an additional transformation of the variables, we can simplify this equation into conformable Burgers' equation. Thus, the Keller Box method is used as a numerical scheme to solve the equation. A comparison is made between numerical results and the analytic solution to validate the results of our proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on developing an efficient numerical approach based on Taylor-wavelets for solving three-point (nonlocal) singular boundary value problems. A special case of the considered problem, with strongly nonlinear source term, arises in thermal explosion in a cylindrical reactor. The existence of a unique solution is thoroughly discussed for the considered problem. To establish the current method, an equivalent integral equation is constructed for the original problem to overcome the singularity at the origin. The evaluation of derivatives appearing in the model is also avoided in this way. Moreover, this scheme skips the integrals while reducing them into a system of nonlinear algebraic equations. Unlike other methods, this new approach does not require any linearization, discretization, perturbation, or evaluation of nonlinear terms separately. To the best of our knowledge, this is the first application of the wavelet-based method to the considered problem. The formulation of the proposed method is further supported by its convergence and error analysis. Some numerical examples are solved to validate the efficiency and robustness of the proposed method. Further, the computational convergence rate (COR) is reported for the first few examples to assist the obtained numerical solution. Moreover, the obtained numerical results are compared with those of existing techniques in the literature. [ABSTRACT FROM AUTHOR]

Despite the variety of methods available to solve nonlinear optimal control problems, numerical methods are still evolving to solve these problems. This paper deals with the numerical solution of nonlinear optimal control affine problems by the interpolated variational iteration method, which was introduced in 2016 to improve the variational iteration method. For this purpose, the optimality conditions are first derived as a two-point boundary value problem and then converted to an initial value problem with the unknown initial values for costates. The speed and convergence of the method are compared with the existing methods in the form of three examples, and the initial values of the costates are obtained by an efficient technique in each iteration. [ABSTRACT FROM AUTHOR]

This paper presents an efficient numerical method to solve two versions of the Duffing equation by the hybrid functions based on the combination of Block-pulse functions and Legendre polynomials. This method reduces the solution of the considered problem to the solution of a system of algebraic equations. Moreover, the convergence of the method is studied. Some examples are given to demonstrate the applicability and effectiveness of the proposed method. Also, the obtained results are compared with some other results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quasilinear reaction diffusion equation with Neumann boundary conditions in a bounded domain. Basing on Sobolev inequality and differential inequality technique, we obtain upper and lower bounds for the blow-up time of the solution. An example is also given to illustrate the abstract results obtained of this paper. [ABSTRACT FROM AUTHOR]

This paper is devoted to the construction of certain polynomials related to Lucas polynomials, namely, modified Lucas polynomials. The constructed modified Lucas polynomials are utilized as basis functions for the numerical treatment of the linear and non-linear second-order boundary value problems (BVPs) involving some specific important problems such as singular and Bratu-type equations. To derive our proposed algorithms, the operational matrix of derivatives of the modified Lucas polynomials is established by expressing the first-order derivative of these polynomials in terms of their original ones. The convergence analysis of the modified Lucas polynomials is deeply discussed by establishing some inequalities concerned with these modified polynomials. Some numerical experiments accompanied by comparisons with some other articles in the literature are presented to demonstrate the applicability and accuracy of the presented algorithms. [ABSTRACT FROM AUTHOR]

The article presents a preparatory stage for solving the thermoelasticity problem for a halfspace with relief. The effect of the relief on diurnal and season variations of the temperature in the upper layer of the crust induced by temperature variations the in atmosphere is studied. The case of weak two-dimensional relief is discussed. In this paper, we say that relief is weak if: (1) the angle of inclination of a relief element to the horizon is small; (2) the thickness d of the heated layer is small compared to the radius of curvature of the line of the relief. For the diurnal mode, we have d ≈ 15 cm, for the seasonal mode, d ≈ 3 m. The heat equation with a boundary condition of the first kind is considered, and an approximate analytical solution is obtained. The results are compared with the numerical solution, which can be considered. The approximate formula gives a satisfactory result if: (1) the angle of inclination of a relief element to the horizon does not exceed 0.2 rad; (2) the curvature of the line of relief does not exceed 2.4 × 10–2 m–1 for the diurnal mode and 1.2 × 10–3 m–1 for the seasonal mode. In this case the relative discrepancy between the numerical and approximate analytical solutions is less then 4% if the depth ≤20d. Temperature variations at a depth of 20d are already almost completely absent: the amplitude does not exceed ~10–9–10–8°C. Therefore, the underlying layers do not significantly effect on displacements and tilts of relief elements located near the surface. [ABSTRACT FROM AUTHOR]

In this paper, a fast scheme for solving unsteady nonlinear convection diffusion problems is proposed and analyzed. At each step, we firstly isolate a nonlinear convection subproblem and a linear diffusion subproblem from the original problem by utilizing operator splitting. By Taylor expansion, we explicitly transform the nonlinear convection one into a linear problem with artificial inflow boundary conditions associated with the nonlinear flux. Then a multistep technique is provided to relax the possible stability requirement, which is due to the explicit processing of the convection problem. Since the self-adjointness and coerciveness of diffusion subproblems, there are so many preconditioned iterative solvers to get them solved with high efficiency at each time step. When using the finite element method to discretize all the resulting subproblems, the major stiffness matrices are same at each step, that is the reason why the unsteady nonlinear systems can be computed extremely fast with the present method. Finally, in order to validate the effectiveness of the present scheme, several numerical examples including the Burgers type and Buckley-Leverett type equations, are chosen as the numerical study. [ABSTRACT FROM AUTHOR]

In a joint work with S. Bianchini [8] (see also [6, 7]), we proved a quadratic interaction estimate for the system of conservation lawsut+fux=0,ut=0=u0x,where u : [0, ∞) × ℝ → ℝn, f : ℝn → ℝn is strictly hyperbolic, and Tot.Var.(u0) ≪ 1. For a wavefront solution in which only two wavefronts at a time interact, such an estimate can be written in the form∑tjinteraction timeσαj−σαj′αjαj′αj+αj′≤CfTot.Var.u02,where αj and αj′ are the wavefronts interacting at the interaction time tj, σ(·) is the speed, |·| denotes the strength, and C(f) is a constant depending only on f (see [8, Theorem 1.1] or Theorem 3.1 in the present paper for a more general form).The aim of this paper is to provide the reader with a proof for such a quadratic estimate in a simplified setting, in which:• all the main ideas of the construction are presented;• all the technicalities of the proof in the general setting [8] are avoided. [ABSTRACT FROM AUTHOR]

In this paper, trigonometrically fitted multi-step hybrid (TFMSH) methods for the numerical integration of oscillatory special second-order initial value problems are proposed and studied. TFMSH methods inherit the frame of multi-step hybrid (MSH) methods and integrate exactly the differential system whose solutions can be expressed as the linear combinations of functions from the set or equivalently the set , where w represents an approximation of the main frequency of the problem. The corresponding order conditions are given and two explicit TFMSH methods with order six and seven, respectively, are constructed. Stability of the new methods is examined and the corresponding regions of stability are depicted. Numerical results show that our new methods are more efficient in comparison with other well-known high quality methods proposed in the scientific literature. [ABSTRACT FROM AUTHOR]

This paper presents the results of numerical simulations of thermal comfort in a passenger coach. The numerical model with people's presence was developed and appropriate boundary conditions were prepared. The ANSYS CFX program was used for the simulations. The calculations were carried out for summer and winter conditions. The predicted mean vote (PMV), predicted percentage dissatisfied (PPD) and draft rate (DR) were calculated to assess the thermal comfort of passengers. The requirements of railway standards in terms of passenger comfort assessment were also verified. Based on the simulation results, it was found that the thermal comfort conditions of the passengers in the coach were not fully satisfactory, especially in summer. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find approximate solutions to the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). The equation is defined by Caputo fractional derivative. A new form of the trial function from the original equation is presented and unknown coefficients in the trial function are computed by using LTCM. Two different initial-boundary value problems are considered as the test problems and approximate solutions are compared with analytical solutions. Numerical results are presented by graphs and tables. From the obtained results, we observe that the method is accurate, effective, and useful. [ABSTRACT FROM AUTHOR]

Foundation scour can have a detrimental effect on the performance of bridge piers, inducing a significant reduction of the lateral capacity of the footing and accumulation of permanent settlement and rotation. Although the hydraulic processes responsible for foundation scour are nowadays well known, predicting their mechanical consequences is still challenging. Indeed, its impact on the failure mechanisms developing around the foundation has not been fully investigated. In this paper, numerical simulations are performed to study the vertical and lateral response of a scoured bridge pier founded on a cylindrical caisson foundation embedded in a layer of dense sand. The sand stress–strain behaviour is reproduced by employing the Severn-Trent model. The constitutive model is firstly calibrated on a set of soil element tests, including drained and undrained monotonic triaxial tests and resonant column tests. The calibration procedure is implemented considering the stress and strain nonuniformities within the samples, by simulating the laboratory tests as boundary value problems. The numerical model is then validated against the results of centrifuge tests. The results of the simulations are in good agreement with the experimental results in terms of foundation capacity and settlement accumulation. Moreover, the model can predict the effects of local and general scour. The numerical analyses also highlight the impact of scouring on the failure mechanisms, revealing that the soil resistance depends on the hydraulic scenario. [ABSTRACT FROM AUTHOR]

This paper provides the 3-D time-dependent analytical solution of the electromagnetic fields and forces emerging if a coil or a permanent magnet moves with a sinusoidal velocity profile relative to a conducting slab of finite thickness. The results can be readily used in application scenarios related to electromagnetic damping, eddy current braking, energy harvesting, or nondestructive testing in order to efficiently analyze diffusion and advection processes in case of harmonic motion. This paper is performed for rectangular and circular coils as well as for cuboidal and cylindrical permanent magnets. The back reaction of the conductor and therewith associated inductive effects are considered. The solutions of the governing equations and the integral expressions for the time-dependent drag and lift force are provided. The analytical results are verified by a comparison with numerical simulations obtained by the finite-element method. The relative difference between the analytically and numerically evaluated force profiles was <0.1%. Exemplary calculations show that the waveforms of both force components strongly depend on the level of constant nominal velocity v0 , the magnitude of the velocity oscillation amplitude v1 , and the underlying oscillation frequency fv . [ABSTRACT FROM AUTHOR]

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping. There are two resolvent estimates for this situation currently in the literature: (i) in the case of elliptic trapping the general "worst case" bound of exponential growth applies, and examples show that this growth can be realized through some sequence of wavenumbers; (ii) in the prototypical case of hyperbolic trapping where the Helmholtz equation is posed in the exterior of two strictly convex obstacles (or several obstacles with additional constraints) the nontrapping resolvent estimate holds with a logarithmic loss. This paper proves the first resolvent estimate for parabolic trapping by obstacles, studying a class of obstacles the prototypical example of which is the exterior of two squares (in two dimensions) or two cubes (in three dimensions), whose sides are parallel. We show, via developments of the vector-field/multiplier argument of Morawetz and the first application of this methodology to trapping configurations, that a resolvent estimate holds with a polynomial loss over the nontrapping estimate. We use this bound, along with the other trapping resolvent estimates, to prove results about integral equation formulations of the boundary value problem in the case of trapping. Feeding these bounds into existing frameworks for analyzing finite and boundary element methods, we obtain the first wavenumber-explicit proofs of convergence for numerical methods for solving the Helmholtz equation in the exterior of a trapping obstacle. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved. A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams. The proposed algorithm, named as two-parameter multiple shooting method, is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions. The impact of the axial force and additional point masses is also taken into account. Due to the fact that the method is based directly on the fourth-order ordinary differential equation, the structures do not have to be divided into many small elements to obtain an accurate enough solution, even though the geometry is very complex. To verify the proposed method, three different examples are considered, i.e., a three-segment non-prismatic beam, a prismatic column subject to non-uniformly distributed compressive loads, and a two-segment beam with an additional point mass. Numerical analyses are carried out with the software MATHEMATICA. The results are compared with the solutions computed by the commercial finite element program SOFiSTiK. Good agreement is achieved, which confirms the correctness and high effectiveness of the formulated algorithm. [ABSTRACT FROM AUTHOR]

Applied element method (AEM) is a recently displacement-based structural analysis method. It provides the benefits of both the finite element method (FEM) and the discrete element method (DEM). This method relies on those structures are segmented into rigid elements linked by normal and shear springs. In this paper a brief note of the AEM is given. Then, using the AEM, a 2D MATLAB open source program was created to analyze different structures with varied boundary conditions and to permit researchers for enhancing the method. The proposed program was verified using linear elastic analysis and large deformation static analysis. The influence of element size and the number of connecting springs between elements was studied. Finally, the proposed program was capable of tracking failed elements and their spread. In addition, the program could predict deflection values and structure deformed shape. [ABSTRACT FROM AUTHOR]

In this paper, a class of second-order singularly perturbed interior layer problems is examined. A nonpolynomial mixed spline is used to develop the tridiagonal scheme. The developed method is second as well as fourthorder accurate based on the parameters. Error analysis is also carried out. The method is shown to converge point-wise to the true solution with higher accuracy. Linear and nonlinear second-order singularly perturbed boundary value problems have been solved by the presented method. Five numerical illustrations are given to demonstrate the applicability of the proposed method. Absolute errors are given in tables, which show that our method is more efficient than previously existing methods. [ABSTRACT FROM AUTHOR]

Analysis of the slipstream development around the high-speed trains in tunnels would provide references for assessing the transient gust loads on trackside workers and trackside furniture in tunnels. This paper focuses on the computational analysis of the slipstream caused by high-speed trains passing through double-track tunnels with a cross-sectional area of 100 m2. Three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations and a realizable k-ε turbulence model were used to describe the airflow characteristics around a high-speed train in the tunnel. The moving boundary problem was treated using the sliding mesh technology. Three cases were simulated in this paper, including two tunnel lengths and two different configurations of the train. The train speed in these three cases was 250 km/h. The accuracy of the numerical method was validated by the experimental data from full-scale tests, and reasonable consistency was obtained. The results show that the flow field around the high-speed trains can be divided into three distinct regions: the region in front of the train nose, the annular region and the wake region. The slipstream development along the two sides of train is not in balance and offsets to the narrow side in the double-track tunnels. Due to the piston effect, the slipstream has a larger peak value in the tunnel than in open air. The tunnel length, train length and length ratio affect the slipstream velocities; in particular, the velocities increase with longer trains. Moreover, the propagation of pressure waves also induces the slipstream fluctuations: substantial velocity fluctuations mainly occur in front of the train, and weaken with the decrease in amplitude of the pressure wave. [ABSTRACT FROM AUTHOR]

The current paper aims at investigating Fractional Hamiltonian Equations for a class of fractional optimal control problems with time delay. Furthermore, we introduce a method to solve the resulting two boundary values problem (TBVP) by extending Agrawal's fractional variational method in (Nonlinear Dyn. 38:323-337, 2004) and using Bernstein polynomials (BPs). In this paper we use the Caputo fractional derivative of order α where $0< \alpha<1$ . Some numerical examples are included to demonstrate the validity of the present method. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical treatment of singularly perturbed delay differential equations having a delay on the first derivative term. The solution of the considered problem exhibits boundary layer behavior on the left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting in an asymptotically equivalent singularly perturbed boundary value problem. The uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper we derive a priori |$L^{\infty }(L^{2})$| and L 2(L 2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall's inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some |$\widehat{T}$|⁠, we derive |$\mathcal{O}$| (h p +1/2) error estimates where the constant factor depends only on |$\widehat{T}$|⁠, but not on the final time T. This can be interpreted as applying Gronwall's inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting). [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified nonlocal boundary value problem method for an homogeneous biharmonic equation in a rectangular domain. We show that the considered problem is ill-posed in the sense of Hadamard, i.e. the solution does not depend continuously on the given data. Convergence estimates for the regularized solution are obtained under a priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The key of the reproducing kernel method (RKM) to solve the initial boundary value problem is to construct the reproducing kernel meeting the homogenous initial boundary conditions of the considered problems. The usual method is that the initial boundary conditions must be homogeneous and put them into space. Another common method is to put homogeneous or non-homogeneous conditions directly into the operator. In addition, we give a new numerical method of RKM for dealing with initial boundary value problems, homogeneous conditions are put into space, and for nonhomogeneous conditions, we put them into operators. The focus of this paper is to further verify the reliability and accuracy of the latter two methods. Through solving three numerical examples of integral-differential equations and comparing with other methods, we find that the two methods are useful. [ABSTRACT FROM AUTHOR]

The aim of this paper is to consider the asymptotic behavior of boundary value problems in n-dimensional domains with periodically placed particles, with a general microscopic boundary condition on the particles and a p-Laplace diffusion operator on the interior, in the case in which the particles are of critical size. We consider the cases in which 1 < p < n, n ≥ 3. In fact, in contrast to previous results in the literature, we formulate the microscopic boundary condition in terms of a Robin type condition, involving a general maximal monotone graph, which also includes the case of microscopic Dirichlet boundary conditions. In this way we unify the treatment of apparently different formulations, which before were considered separately. We characterize the so called "strange term" in the homogenized problem for the case in which the particles are balls of critical size. Moreover, by studying an application in Chemical Engineering, we show that the critically sized particles lead to a more effective homogeneous reaction than noncritically sized particles. [ABSTRACT FROM AUTHOR]

Motivated by the work [9], in this paper we investigate the infinite boundary value problem associated with the semilinear PDE Lu = ƒ(u) + h(x) on bounded smooth domains Ω ⊆ ℝn, where L is a non-divergence structure uniformly elliptic operator with singular lower-order terms. In the equation, ƒ is a continuous non-decreasing function that satisfies the Keller–Osserman condition, while h is a continuous function in Ω that may change sign, and which may be unbounded on Ω. Our purpose is two-fold. First we study some sufficient conditions on ƒ and h that would ensure existence of boundary blow-up solutions of the above equation, in which we allow the lower-order coefficients to be singular on the boundary. The second objective is to provide sufficient conditions on ƒ and h for the uniqueness of boundary blow-up solutions. However, to obtain uniqueness, we need the lower-order coefficients of L to be bounded in Ω, but we still allow h to be unbounded on Ω. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities. [ABSTRACT FROM AUTHOR]

This paper presents the solution of the initial boundary-value problem for the system of 1-D thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, we study the following boundary value problem involving the weak p-Laplacian where is the Sierpiński gasket in , is its boundary, , , and are appropriate functions. We will show the existence of a nontrivial weak solution to the above problem for a certain range of using the analysis of fibering maps on suitable subsets. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered. [ABSTRACT FROM AUTHOR]

In this paper internal boundary value problem of elastic equilibrium of the homogeneous isotropic body bounded by coordinate lines of the parabolic coordinate system is considered, when on the parabolic border normal stress is given. The exact solution is obtained by the method of separation of variables. Using the MATLAB software, the numerical results are obtained at some characteristic points of the body and relevant 2D and 3D graphs are presented. [ABSTRACT FROM AUTHOR]

In the present paper, we explicitly solve, in the form of absolutely and uniformly convergent series, a two-dimensional boundary value problem of statics in linear theory elasticity for an isotropic elastic disk consisting of empty pores. The uniqueness theorem for the solution is proved. For a particular problem numerical results are given. [ABSTRACT FROM AUTHOR]

This paper deals with the functional relation between multivariate methods of canonical correlation analysis (CCA), partial least squares (PLS) and also their kernelized versions. Both methods are determined by the solution of the respective optimization problem, and result in algorithms using spectral or singular decomposition theories. The solution of the parameterized optimization problem, where the boundary points of a parameter give exactly the results of CCA (resp. PLS) method leads to the vector functions (paths) of eigenvalues and eigenvectors or singular values and singular vectors. Specifically, in this paper, the functional relation means the description of classes into which the given paths belong. It is shown that if input data are analytical (resp. smooth) functions of a parameter, then the vector functions are also analytical (resp. smooth). Those approaches are studied on three practical examples of European tourism data. [ABSTRACT FROM PUBLISHER]

This paper studies the second-order asymptotics of the Gaussian multiple-access channel with degraded message sets. For a fixed average error probability $ \varepsilon \in (0,1)$ and an arbitrary point on the boundary of the capacity region, we characterize the speed of convergence of rate pairs that converge to that boundary point for codes that have asymptotic error probability no larger than $ \varepsilon $ . As a stepping stone to this local notion of the second-order asymptotics, we study a global notion, and establish relationships between the two. We provide a numerical example to illustrate how the angle of approach to a boundary point affects the second-order coding rate. This is the first conclusive characterization of the second-order asymptotics of a network information theory problem in which the capacity region is not a polygon. [ABSTRACT FROM PUBLISHER]