Higher order operator splitting methods via Zassenhaus product formula: Theory and applications

In this paper, we contribute higher order operator splitting methods improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order operator splitting methods is presented. While applying the methods to partial differential equations, the benefits of balancing time and spatial scales are discussed to accelerate the methods.The verification of the improved splitting methods are done with numerical examples. An individual handling of each operator with adapted standard higher order time-integrators is discussed. Finally, we conclude the higher order operator splitting methods.