Splitting Method of Convection-Diffusion Methods with Disentanglement methods

Abstract

In this paper, we discuss higher-order operator-splitting methods done by disentanglement methods. The idea is based on computing best fitted exponents to an exponential splitting scheme with more than two operators. We introduce the underlying splitting methods and the special scheme to compute the disentanglement method. First applications are done to consider finite difference methods to the spatial operators and derive their underlying Lie algebras. Based on the Lie algebra it is simple to compute the corresponding Lie group with $\exp$ functions. Such results help to derive the disentanglement of the operator splitting method. The verification of our improved splitting methods are done with first numerical examples.