Operator Splittings and Numerical Methods

摘要

The operator splitting method is a widely used technique which is frequently applied to the solution of complex problems. However, its application is not enough to the practical solution of the problems. The split sub-problems still require some numerical method. In this paper we give a unified investigation of the operator splitting and the numerical discretization. Moreover, we consider the interaction of the operator splitting method and the applied numerical methods to the solution of the different sub-processes. We show that many well-known fully-discretized numerical schemes to solving the Cauchy problems can be obtained in this manner. We investigate the convergence of these methods, too.