Crank–Nicolson finite difference method for two-dimensional diffusion with an integral condition

摘要

A finite difference method which is based on the (5,5) Crank–Nicolson (CN) scheme is developed for solving the heat equation in two-dimensional space with an integral condition replacing one boundary condition. The fully implicit method developed here, is unconditionally stable and it has reasonable accuracy. While the conditionally stable fully explicit schemes use less amount of central processor (CPU) time; the unconditional stability of the scheme developed in this article for every diffusion number is significant. Some numerical tests are presented and the accuracy obtained and the CPU time required are reported. Error estimates derived in the maximum norm are tabulated.