Weighted Iterative Operator-Splitting Methods: Stability-Theory

摘要

In the last years the need to solve complex physical models increased. Because of this motivation to solve complex models with efficient methods, we deal with advanced operator-splitting methods. They are based on weighted iterative operator-splitting methods and decouple complicate problems in simpler problems. The stability of the weighted splitting method is discussed and the efficiency of such methods. For the stiff-problems we present the A-stability property and the choice of the weighted parameters. The theory for the semi-discretized equations is introduced with respect to the gained ODE's. A general stability-theory for linearized operators is proposed and discussed for stiff-problems. Finally we concern the weighted operator-splitting methods for multi-dimensional and multi-physical problems.