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2020•Journal Plus EducationOpen access

A Finite Difference Approach to the Solution of Elliptic Boundary value Problems with Nonlocal Boundary Condition in PDEs

Pramod Kumar Pandey

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Abstract

In the article Poisson equation and corresponding boundary value problem with nonlocal boundary condition in two dimension space is considered. A numerical technique based on the finite difference method is proposed for the approximate solution of a considered problem. The computational results in numerical experiment on linear and nonlinear model test problems are presented to validate the proposed idea. Theoretically analyzed and established the convergence of the proposed method.

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What this paper is about

In the article Poisson equation and corresponding boundary value problem with nonlocal boundary condition in two dimension space is considered. A numerical technique based on the finite difference method is proposed for the approximate solution of a considered problem. The computational results in numerical experiment on linear and nonlinear model test problems are presented to validate the proposed idea. Theoretically analyzed and established the convergence of the proposed method.

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Available abstract

In the article Poisson equation and corresponding boundary value problem with nonlocal boundary condition in two dimension space is considered. A numerical technique based on the finite difference method is proposed for the approximate solution of a considered problem. The computational results in numerical experiment on linear and nonlinear model test problems are presented to validate the proposed idea. Theoretically analyzed and established the convergence of the proposed method.

Key concepts: Mathematics, Boundary value problem, Mathematical analysis, Convergence (economics), Mixed boundary condition, Finite difference method, Dimension (graph theory), Poincaré–Steklov operator

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