A finite difference method for a non-local boundary value problem for two-dimensional heat equation

摘要

A second-order finite difference scheme is given for the numerical solution of a two-dimensional non-local boundary value problem for heat equation. Using a suitable transformation, the solution of this problem is equivalent to the solution of two other problems. The first problem which is a one-dimensional non-local boundary value problem giving the value of μ through using a second-order finite difference scheme. Using this result, the second problem will be changed to a classical two-dimensional problem with Nuemann's boundary condition which will be solved numerically. The stability properties and truncation error of the new method are discussed and the results of numerical experiments are presented.