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 |
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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) |
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