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

This paper presents some new techniques in designing 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 (m is a positive integer) by Saulʹyev asymmetric schemes. The algorithm can increase the stability bounds of the classical explicit method by 2m times, 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.