Linear and Quasi-Linear Iterative Splitting Methods

Abstract

In this paper we consider time-decomposition methods and present interesting model problems as benchmark problems in order to study the numerical analysis of the proposed methods. For the time-decomposition methods we discuss the iterative operator-splitting methods with re- spect to the stability and consistency. The main idea for deriving the error estimates is the Taylor expansion in time of the linearized opera- tors. The stability analysis is based on the A-stability of ordinary differ- ential equations, and the importance of including weighted parameters for relaxing the iterative operator-splitting methods can be seen. The exactness and the effciency of the methods are investigated through so- lutions of nonlinear model problems of parabolic differential equations, for example systems of convection-reaction-discussion equations. Finally we discuss the future works and the usefulness of this study in real-life applications. Mathematics Subject