Numerical integrators based on the Magnus expansion for nonlinear dynamical systems

M. Hajiketabi and F. Casas

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: Explicit numerical integration algorithms up to order four based on the Magnus expansion for nonlinear non-autonomous ordinary differential equations are presented and tested on problems possessing qualitative (very often, geometric) features that is convenient to preserve under numerical discretization. The range of applications covers augmented dynamical systems, highly oscillatory problems and nonlinear non-autonomous partial differential equations of evolution previously discretized in space.

Keywords: Magnus expansion; Lie-group methods; Preserving properties; Augmented systems; High oscillation; Non-autonomous PDEs of evolution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308367

DOI: 10.1016/j.amc.2019.124844

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