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Numerical preservation of multiple local conservation laws

Frasca-Caccia, Gianluca, Hydon, Peter E. (2021) Numerical preservation of multiple local conservation laws. Applied Mathematics and Computation, 403 . Article Number 126203. ISSN 0096-3003. E-ISSN 1873-5649. (doi:10.1016/j.amc.2021.126203) (KAR id:87360)

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Official URL
http://dx.doi.org/10.1016/j.amc.2021.126203

Abstract

There are several well-established approaches to constructing finite difference schemes that preserve global invariants of a given partial differential equation. However, few of these methods preserve more than one conservation law locally. A recently-introduced strategy uses symbolic algebra to construct finite difference schemes that preserve several local conservation laws of a given scalar PDE in Kovalevskaya form. In this paper, we adapt the new strategy to PDEs that are not in Kovalevskaya form and to systems of PDEs. The Benjamin-Bona-Mahony equation and a system equivalent to the nonlinear Schroedinger equation are used as benchmarks, showing that the strategy yields conservative schemes which are robust and highly accurate compared to others in the literature.

Item Type: Article
DOI/Identification number: 10.1016/j.amc.2021.126203
Uncontrolled keywords: Finite difference methods, discrete conservation laws, BBM equation, nonlinear Schroedinger equation, energy conservation, momentum conservation
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Hydon
Date Deposited: 28 Mar 2021 16:22 UTC
Last Modified: 26 Mar 2022 00:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/87360 (The current URI for this page, for reference purposes)
Frasca-Caccia, Gianluca: https://orcid.org/0000-0002-4703-1424
Hydon, Peter E.: https://orcid.org/0000-0002-3732-4813
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