A new high order iterative alternating decomposition explicit method to solve the heat conduction equation

Abstract

In this paper, a new iterative alternating decomposition explicit (lADE) scheme of order of accuracy similar to that of Sahimi et al. (1993) of the Mitchell-Fairweather variant is developed to solve the one-dimensional parabolic problem. It is based on the two-stage fractional splitting strategy suggested by D'Yakonov and our numerical experiments indicate that the method is more accurate than the recently developed Alternating Group Explicit (AGE) method of Peaceman-Rachford variant.