Search

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]

In this paper, septic spline is defined for interpolation at equally spaced knots along with the end conditions required to complete the definition of spline. These conditions are in terms of given functional values at the knots and lead to uniform convergence of O ( h 8 ), throughout the interval of interpolation. The main objective of defining the end conditions for septic spline is to use the septic spline for the solutions of sixth-order boundary value problems, being discussed in the subsequent paper. [ABSTRACT FROM AUTHOR]

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we analyse a ν-th order, , discrete fractional three-point boundary value problem (BVP). We show that Green's function associated to this problem satisfies certain conditions. We demonstrate that the range of admissible boundary conditions depends upon the order ν of the difference equation, and we give explicit formulae for this dependence. By using both the Brouwer fixed point theorem and the Krasnosel'skiĭ fixed point theorem, we then show that a solution to this problem exists. Our results extend recent results on discrete fractional BVPs (FBVPs), and they also provide an initial set of results on the theory of multipoint FBVPs on the time scale of integers. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of nonlinear difference equations subject to global nonlinear boundary conditions. We provide sufficient conditions for the existence of solutions based on properties of the nonlinearities and the eigenvalues of an associated linear Sturm–Liouville problem. [ABSTRACT FROM AUTHOR]

This study deals with the exact buckling solutions of annular plates with an elastically restrained guided edge against translation. The classical plate theory is used to derive the governing differential equation for annular plate with elastically restrained guided edge against translation. The buckling mode may not be axisymmetric as previously assumed. In certain cases, an asymmetric mode would yield a lower buckling load. This is due to switching of mode. This work presents the critical buckling load parameters for axisymmetric and asymmetric buckling modes. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational restraints, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic annular plates. The numerical results obtained, are in good agreement with the previously published data. In this paper the characteristic equations are exact, therefore the results can be calculated to any accuracy. Comparison of studies demonstrates the accuracy and stability of this work. [ABSTRACT FROM AUTHOR]

In this paper, to find an approximate solution of general linear Fredholm integro-differential–difference equations (FIDDEs) under the initial-boundary conditions in terms of the Bessel polynomials, a practical matrix method is presented. The idea behind the method is that it converts FIDDEs to a matrix equation which corresponds to a system of linear algebraic equations and is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. The solutions are obtained as the truncated Bessel series in terms of the Bessel polynomials J n (x) of the first kind defined in the interval [0, ∞). The error analysis and the numerical examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

This paper introduces the implementation of complex frequency shifted perfectly matched layer (CFS-PML) absorbing boundary conditions for the unconditionally stable finite-difference Laguerre time-domain (FDLTD) method. It has been shown that the relative performance of the CFS-PML implementations is superior to the PML and Mur ABCs performance by an example. [ABSTRACT FROM AUTHOR]

In this paper, we construct a group of Saul'yev type asymmetric difference formulas for the dispersive equation. Based on these formulas we derive a new alternating 6-point group algorithm to solve dispersive equations with periodic boundary conditions. The algorithm has a high-order accuracy in space and an unconditional stability. The theoretical results are conformed to the numerical simulation. A comparison of this algorithm with the previous Alternating Group Explicit method is presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose an original numerical approach for parabolic problems whose governing equations are defined on unbounded domains. We are interested in studying the class of problems admitting invariance property to Lie group of scalings. Thanks to similarity analysis the parabolic problem can be transformed into an equivalent boundary value problem governed by an ordinary differential equation and defined on an infinite interval. A free boundary formulation and a convergence theorem for this kind of transformed problems are available in [R. Fazio, A novel approach to the numerical solution of boundary value problems on infinite intervals, SIAM J. Numer. Anal. 33 (1996), pp. 1473-1483]. Depending on its scaling invariance properties, the free boundary problem is then solved numerically using either a noniterative, or an iterative method. Finally, the solution of the parabolic problem is retrieved by applying the inverse map of similarity. [ABSTRACT FROM AUTHOR]

In this paper, the upper and lower solution method and monotone iterative technique are employed to study the boundary value problem for a class of first-order impulsive ordinary differential equations with Caratheodory condition on infinite intervals. Several existence theorems are obtained. [ABSTRACT FROM AUTHOR]

A vertex subversion strategy of a graph G is a set of vertices X⊆ V(G) whose closed neighbourhood is deleted from G. The survival subgraph is denoted by G/X. The vertex-neighbour-integrity of G is defined to be VNI(G)=min{|X|+τ(G/X):X⊆ V(G)}, where τ(G/X) is the maximum order of the components of G/X. This graph parameter was introduced by Cozzens and Wu to measure the vulnerability of spy networks. Gambrell proved that the decision problem of computing the vertex-neighbour-integrity of a graph is NP-complete. In this paper we evaluate the vertex-neighbour-integrity of the composition graphs of paths and cycles. [ABSTRACT FROM AUTHOR]

In this paper, by the Alexandrov-Serrin method of moving plane combined with integral inequalities, we prove some new Liouville type results for positive solution of semilinear elliptic system in the whole space N. [ABSTRACT FROM AUTHOR]

This paper deals with discrete second order Sturm-Liouville problems where the parameter that is part of the Sturm-Liouville difference equation appears nonlinearly in the boundary conditions. The operator is extended to a self-adjoint operator and an expansion theorem is proved. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the existence of extremal solutions to a first-order initial value problem on an interval of an arbitrary time scale. We prove the existence of extremal solutions for problems satisfying Carathéodory's conditions. Moreover, they are approximated uniformly by a sequence of lower and upper solutions to this problem, respectively. We also can warrant the existence and approximation of extremal solutions for the problem by relaxing their continuity properties. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of an eigenvalue interval of solutions to the singular discrete boundary value problem ... where our nonlinearity may be singular in its dependent variable and is allowed to change sign. [ABSTRACT FROM AUTHOR]

In this paper a sextic spline is defined for interpolation at equally spaced knots along with the end conditions required to complete the definition of the spline. These conditions are in terms of given functional values at the knots and lead to uniform convergence of O(h7) throughout the interval of interpolation. The main objective of defining the end conditions for the sextic spline is to use the sextic spline not only for interpolation purposes, but also for the solution of the fifth-order boundary value problem, with the change consistent with the boundary value problem.†Dedicated to the memory of Dr. M. Rafique. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is suggested to solve a class of boundary value problems (BVPs) for a weakly coupled system of singularly perturbed second-order ordinary differential equations of convection-diffusion type. First, in this method, an asymptotic expansion approximation of the solution of the BVP is constructed by using the basic ideas of a well known perturbation method namely Wentzal, Kramers and Brillouin (WKB). Then, some initial value problems (IVPs) are constructed such that their solutions are the terms of this asymptotic expansion. These problems happen to be singularly perturbed problems and, therefore, exponentially fitted finite difference schemes are used to solve these problems. As the BVP is converted into a set of IVPs and an asymptotic expansion approximation is used, the present method is termed as asymptotic initial-value method. The necessary error estimates are derived and examples provided to illustrate the method. [ABSTRACT FROM AUTHOR]