Additive splitting methods for parallel solution of evolution problems

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Date
2020
Volume
2767
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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Keywords
Splitting method, Richardson extrapolation, nonlinear Schrödinger equation, nonlinear optics
Citation
Amiranashvili, S., Radziunas, M., Bandelow, U., Busch, K., & Čiegis, R. (2020). Additive splitting methods for parallel solution of evolution problems (Vol. 2767). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2767
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