Explicit time marching method with enhanced stability.

Recent developments in distributed computing architecture are slowly changing the way we develop partial differential equation solvers for simulating complex industrial and natural systems. Since achieving perfect parallelization of implicit temporal schemes is quite challenging, there is a growing interest in using explicit procedures with enhanced stability limits. The current work focuses on one such enhancement obtained by modifying an asynchronous delayed difference method. The proposed scheme, called the weighted difference scheme, is obtained as a weighted average of the delayed and conventional explicit schemes. This method exhibits an improved stability limit of 1.5 and also helps overcome the checkerboard instability associated with the delayed difference scheme. In the current paper, we discuss the different attributes of the proposed weighted scheme using a series of numerical analyses.