Objectives . A finite-difference computational algorithm is proposed for solving a mixed boundary-value problem the Poisson equation given in two-dimensional irregular domains. Methods To solve problem, generalized curvilinear coordinates are used. The physical domain mapped to (unit square) space of coordinates. original written and approximated on uniform grid domain.The obtained results non-...

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

In this paper, the direct method is utilized for solving second order two-point boundary value problem of Neumann type. The method will obtain the solution of the second order boundary value problem directly without reducing it to to first order equations. The method will be implemented using variable step size via shooting technique adapted with the Newton method. Numerical results are given t...

Parallelization of the algebraic ctitious domain method is considered for solving Neumann boundary value problems with variable coeecients. The resulting method is applied to the parallel solution of the subsonic full potential ow problem which is linearized by the Newton method. Good scalability of the method is demonstrated in Cray T3E distributed memory parallel computer using MPI in communi...

We consider singular perturbed eigenvalue problem for Laplace operator in a two-dimensional domain. In the boundary we select a set depending on a character small parameter and consisting of a great number of small disjoint parts. On this set the Dirichlet boundary condition is imposed while on the rest part of the boundary we impose the Neumann condition. For the case of homogenized Neumann or...

The purpose of this paper is to construct the solution of self-adjoint boundary value problems on finite networks. To this end, we obtain explicit expressions of the Green functions for all different boundary value problems. The method consists in reducing each boundary value problem either to a Dirichlet problem or to a Poisson equation on a new network closely related with the former boundary...

A new method is introduced for studying boundary value problems for a class of linear PDEs with variable coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs with constant coefficients. As illustrative examples the following boundary value problems are solved: (a) A Dirichlet and a Neumann problem on the half line for th...

Abstract. We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in R via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explic...

In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...