Additive splitting methods for parallel solutions of evolution problems

Abstract

We demonstrate how a multiplicative splitting method of order $P$ can be utilized to construct an additive splitting method of order $P+3$. The weight coefficients of the additive method depend only on $P$, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis of a test problem, and numerical examples with special discussion of the parallelization properties and applications to nonlinear optics.