An analysis of numerical solution of diffusion equation with nonlocal boundary condition

Aim of the paper is to develop finite difference method for solving the heat equation in two- dimensional space with non-local boundary condition. An explicit second order forward time centered method is considered which is well suited for parabolic partial differential equation with continuous boundary conditions. Suitability of the method is presented through an example and relative error is determined. Also Adomian decomposition method has been used to find analytical solution of the problem.