The paper deals with the two-dimensional exterior boundary value problems of the steady-state oscillation theory for anisotropic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld–Kupradze type are established. Uniqueness theorems of the basic and mixed type bound...

The problem of computing singular and hypersingular integrals involved in a large class of boundary value problems is considered. The method is based on Green’s theorem for calculating the diagonal elements of the resulting discretized matrix using the Nyström discretization method. The method is successfully applied to classical boundary value problems. Convergence of the method is also discus...

We introduce an algorithm for the eecient numerical solution of exterior boundary value problems for the Helmholtz equation. The problem is reformulated as an equivalent one on a bounded domain using an exact non-local boundary condition on a circular artiicial boundary. An FFT-based fast Helmholtz solver is then derived for a nite-element discretization on an annular domain. The exterior probl...

The capacitance matrix method has been widely used as an e cient numerical tool for solving the boundary value problems on irregular regions. Initially, this method was based on the Sherman-Morrison-Woodbury formula, an expression for the inverse of the matrix (A+UVT ) with A 2 <n n and U;V 2 <n p. Extensions to the capacitance matrix method with restrictive assumptions on the matrices A and (A...

| Matrix decomposition algorithms employing fast Fourier transforms were developed recently by the authors to solve the systems of linear algebraic equations that arise when piecewise Hermite bicubic orthogonal spline collocation (OSC) is applied to certain separable elliptic boundary value problems on a rectangle. In this paper, these algorithms are interpreted as Fourier methods in analogy wi...

In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary condit...

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express th...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...