Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition

Three fully explicit finite difference schemes, the standard FTCS method and the 9-point finite difference scheme and the fully explicit technique were applied to the two-dimensional diffusion equation with an integral condition replacing one-boundary condition. The latter was suitable for two-dimensional diffusion with an integral condition because of its fourth-order accuracy. These methods were found suitable for parabolic partial differential equations with continuous boundary conditions. Use of these methods gave acceptable results and implied that the convergence to the exact solution when 'h' reached zero.