Pure alternating segment explicit-implicit method for the diffusion equations

Abstract

In this paper, a special class of Hopscotch Algorithms for the finite difference solution of the diffusion equation is considered. The algorithm is very efficient with regard to parallel computing in MIMD and ease of programming. A better convergence of the difference solution is proved without the conditions of either Δt/Δx 2 = C or Δt/Δx→0 as Δt→ 0 and Δx→0. Numerical examples of the method are included.