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

A second-order finite difference scheme is given for the numerical solution of a two-dimensional non-local boundary value problem for heat equation. U sing a suitable transformation, the solution of this problem is equivalent to the solution of two other problems. The first problem which is a one-dim ensional non-local boundary value problem giving the value of mu through us ing 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 prope rties and truncation error of the new method are discussed and the results of numerical experiments are presented. (C) 2000 Elsevier Science Inc. All rights reserved.