Error Analysis Through Energy Minimization and Stability Properties of Exponential Integrators

Odysseas Kosmas () and Dimitrios Vlachos ()
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Odysseas Kosmas: The University of Manchester
Dimitrios Vlachos: University of Peloponnese

A chapter in Nonlinear Analysis and Global Optimization, 2021, pp 295-307 from Springer

Abstract: Abstract In this article, the stability property and the error analysis of higher-order exponential variational integration are examined and discussed. Toward this purpose, at first we recall the derivation of these integrators and then address the eigenvalue problem of the amplification matrix for advantageous choices of the number of intermediate points employed. Obviously, the latter determines the order of the numerical accuracy of the method. Following a linear stability analysis process we show that the methods with at least one intermediate point are unconditionally stable. Finally, we explore the behavior of the energy errors of the presented schemes in prominent numerical examples and point out their excellent efficiency in long term integration.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-61732-5_13

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DOI: 10.1007/978-3-030-61732-5_13

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