Abstract: The partial differential equation studied was first transformed into the ordinary differential equations, and then the Trotter product formula of exponential function was used to approximate the coefficientmatrix of these ordinary differential equations. The coefficient matrix was separated into smallblock matrixes, and CrankNicolson method was used to obtain results. So a new difference scheme of variable coefficient diffusion equation was thus obtained. It is an explicit difference scheme with simple calculation and unconditional stability. Some properties of this scheme were discussed. Subsequent numerical experiment shows that the presented method possesses simple calculation and high accuracy.

Key words: variable coefficient diffusion equation, modified local CrankNicolson method, stability, numerical accuracy