WIAS Preprint No. 2767, (2020)

Additive splitting methods for parallel solution of evolution problems


Authors

  • Amiranashvili, Shalva
    ORCID: 0000-0002-8132-882X
  • Radziunas, Mindaugas
    ORCID: 0000-0003-0306-1266
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • Busch, Kurt
  • Čiegis, Raimondas

2010 Mathematics Subject Classification

  • 41A25 65N12 65Y20 65Y05 68Q25 68W10

Keywords

  • Splitting method, Richardson extrapolation, nonlinear Schrödinger equation, nonlinear optics

DOI

10.20347/WIAS.PREPRINT.2767

Abstract

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.

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