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A New Technique for Preserving Conservation Laws

Frasca-Caccia, Gianluca, Hydon, Peter E. (2021) A New Technique for Preserving Conservation Laws. Foundations of Computational Mathematics, . ISSN 1615-3375. E-ISSN 1615-3383. (doi:10.1007/s10208-021-09511-1) (KAR id:88284)

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Abstract

This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev–Petviashvili equation.

Item Type: Article
DOI/Identification number: 10.1007/s10208-021-09511-1
Uncontrolled keywords: Finite difference methods, Conservation laws, Boussinesq equation, pKP equation, Invariant 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: 20 May 2021 18:44 UTC
Last Modified: 14 Apr 2022 22:08 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/88284 (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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