Weighted Iterative Operator-Splitting Methods for stiff problems and applications

Abstract

In this paper we describe advanced operator-splitting methods for more accurate and exact decoupling of stiff systems. We deal with stiff operators and contribute for both stiff operators a new weighted iterative operator-splitting method. Based on the stabilization theory for stiff systems, we developed our weighting method. The idea behind is a combination of first order and higher order operator splitting methods. We discuss our methods in well-known test-problems for systems of ordinary-differential equations and compare with the exact solutions of the systems. Finally we present an application to a convection-reaction equation with stiff reaction-term. We end with a discuss for modifying our methods for multi-dimensional and multi-physical problems.