Explicit solution of two-dimensional diffusion subject to specification of mass

An explicit finite difference scheme for the numerical solution of the diffusion equation on a rectangular region, subject to a non-local boundary condition in the form of a double integral which simulates the specificaion of mass in a curved region is developed. The scheme, is based on the two-dimensional 5-point Forward-time Centered-Space (FTCS) explicit formula. This method is simple in structure, is economical to use and is second-order, with a bounded range of stability. Some numerical tests are presented and the accuracy obtained and the CPU times required are compared to those found using the method described by Cannon, Lin and Matheson.