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01-06-2022

Composite symmetric second derivative general linear methods for Hamiltonian systems

Authors: Behnaz Talebi, Ali Abdi, Gholamreza Hojjati

Published in: Calcolo | Issue 2/2022

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Abstract

Symmetric second derivative general linear methods (SGLMs) have been already introduced for the numerical solution of time-reversible differential equations. To construct suitable high order methods for such problems, the newly developed composition theory has been successfully used for structure-preserving methods. In this paper, composite symmetric SGLMs are introduced using the generalization of composite theory for general linear methods. Then, we construct symmetric methods of order six by the composition of symmetric SGLMs of order four. Numerical results of the constructed methods verify the theoretical order of accuracy and illustrate that the invariants of motion over long time intervals for reversible Hamiltonian systems are well preserved.

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Title: Composite symmetric second derivative general linear methods for Hamiltonian systems
Authors: Behnaz Talebi
Ali Abdi
Gholamreza Hojjati
Publication date: 01-06-2022
Publisher: Springer International Publishing
Published in: Calcolo / Issue 2/2022
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-022-00458-5

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