The DʹYakonov fully explicit variant of the iterative decomposition method

In this paper, a new iterative alternating decomposition (IADE) scheme of (4,2) order of accuracy is developed to solve the one-dimensional parabolic problem. It is based on the two-stage fractional splitting strategy suggested by DʹYakonov and found to be generally more accurate than the recently developed (2,2) accurate alternating group explicit (AGE) method of Peaceman-Rachford variant. As the method is fully explicit, its feature can be fully utilized for parallelization by means of a domain decomposition strategy.