Crank-Nicolson finite difference method for two-dimensional diffusion withan integral condition

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 impl icit method developed here, is unconditionally stable and it has reasonable accuracy. While the conditionally stable fully explicit schemes use less a mount of central processor (CPU) time; the unconditional stability of the s cheme developed in this article for every diffusion number is significant. Some numerical tests are presented and the accuracy obtained and the CPU ti me required are reported. Error estimates derived in the maximum norm are t abulated. (C) 2001 Elsevier Science Inc. All rights reserved.