 Structure preserving algorithms with adaptive time step for Birkhoffian systemsXinlei Kong, Yinjie Song and Huibin Wu Applied Mathematics and Computation, 2024, vol. 480, issue C Abstract: Structure preserving algorithms with adaptive time step are systematically developed for Birkhoffian systems. The development mainly consists of construction, implementation, and application of this kind of algorithms. The construction is based on a direct discretization of the Pfaff–Birkhoff principle in which time is treated as a dynamical variable particularly. The resulting discrete Birkhoffian equations then determine a numerical algorithm for iteration which automatically meets the requirement of structure preservation and time step adaptation. Following the construction, an alternative optimization technique of solving discrete Birkhoffian equations and a reasonable method for initialization of the simulation are provided subsequently, for practical implementation of the algorithm. The performance of the developed algorithm is examined finally by preliminary application in typical examples. Numerical results indicate that the time step adaptation leads to a much improved performance on precisely preserving conserved quantities. Keywords: Birkhoffian dynamics; Structure preserving algorithms; Adaptive time step; Noether's theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003825 DOI: 10.1016/j.amc.2024.128921 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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