New techniques in designing finite difference domain decomposition algorithm for the heat equation

Abstract

This paper presents a new technique in designing the finite difference domain decomposition algorithm for the heat-equation. The basic procedure is to define the finite difference schemes at the interface grid points with smaller time step Δt̄ = Δt̄/m (m is a positive integer) by the classical explicit scheme. The stability region of the algorithm is expanded m times comparing with the classical explicit scheme, and the prior error estimates for the numerical solutions are obtained for some algorithms when m = 2 or m = 3. Numerical experiments on stability and accuracy are also presented. © Springer-Verlag Berlin Heidelberg 2004.