New versions of iterative splitting methods for the momentum equation

Abstract

In this paper we propose some modifications in the schemes for the iterative splitting techniques defined in Geiser (2009) for partial differential equations and introduce the parallel version of these modified algorithms. Theoretical results related to the order of the iterative splitting for these schemes are obtained. In the numerical experiments we compare the obtained results by applying iterative methods to approximate the solutions of the nonlinear systems obtained from the discretization of the splitting techniques to the mixed convection–diffusion Burgers’ equation and a momentum equation that models a viscous flow. The differential equations in each splitting interval are solved by the back-Euler–Newton algorithm using sparse matrices.