Abstract
Partial differential equations with nonlocal boundary conditions have been widely applied in various fields of science and engineering. In this work, we first build a high accuracy difference scheme for Poisson equation with two integral boundary conditions. Then, we prove that the scheme can reach the asymptotic optimal error estimate in the maximum norm through applying the discrete Fourier transformation. In the end, numerical experiments validate the correctness of theoretical results and show the stability of the scheme.
Highlights
Partial differential equations with nonlocal boundary conditions have been widely used to build mathematical models in various fields of science and engineering such as thermoelasticity, physics, medical science, chemical engineering, and so on.This work is concerned with the following two-dimensional Poisson equation with two integral boundary conditions: ⎧ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨u = f (x, y), u|x=0 = μ1(y),(x, y) ∈ = (0, 1)2, 0 < y < 1, ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ u|x=1 ξ1 0 u 1 ξ2 u= μ2(y), dy = μ3(x), dy = μ4(x)
In [10, 11], the authors presented some iterative methods for the system of difference equations to solve nonlinear elliptic equation with integral condition
The radial basis function (RBF) collocation method is very popular for PDEs to seek numerical solution, especially for elliptic equations with nonlocal boundary [14,15,16]
Summary
This work is concerned with the following two-dimensional Poisson equation with two integral boundary conditions: Sapagovas [7] presented a difference scheme of fourth-order approximation for Poisson equation with two integral boundary conditions. Berikelashvili [8] constructed some difference schemes for Poisson problem with one integral condition and obtained its estimate of the convergence rate.
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