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Additive splitting methods for parallel solution of evolution problems
2020, Amiranashvili, Shalva, Radziunas, Mindaugas, Bandelow, Uwe, Busch, Kurt, Čiegis, Raimondas
We demonstrate how a multiplicative splitting method of order P can be used 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, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.