A time‐splitting finite difference method for two‐dimensional diffusion with an integral condition

Abstract

AbstractA new fourth‐order locally one‐dimensional (LOD) finite difference scheme based upon the Noye‐Hayman method for one‐dimensional diffusion is used to solve a two‐dimensional time‐dependent diffusion equation with an integral condition replacing one boundary condition. Numerical testing shows this gives better results than a locally one‐dimensional scheme based on the classical forward‐time centred‐space (FTCS) method for one‐dimensional diffusion except when the diffusion number is 1/6 and the methods are identical. Results from some numerical experiments are presented.