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Locally conservative finite difference schemes for the Modified KdV equation

Frasca-Caccia, Gianluca, Hydon, Peter E. (2019) Locally conservative finite difference schemes for the Modified KdV equation. Journal of Computational Dynamics, 6 (2). pp. 307-323. ISSN 2158-2491. E-ISSN 2158-2505. (doi:10.3934/jcd.2019015) (KAR id:76694)

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Finite diffrence schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic nonlinearity. In principle, a simplified version of the direct approach also works for equations with polynomial nonlinearity of higher degree. For the Modified Korteweg-de Vries equation, whose nonlinear term is cubic, this approach yields several new families of second-order accurate schemes that preserve mass and either energy or momentum. Two of these families contain Average Vector Field schemes of the type developed by Quispel and co-workers. Numerical tests show that each family includes schemes that are highly accurate compared to other mass-preserving methods that can be found in the literature.

Item Type: Article
DOI/Identification number: 10.3934/jcd.2019015
Uncontrolled keywords: Finite difference methods, conservation laws
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: 22 Sep 2019 16:13 UTC
Last Modified: 08 Dec 2022 22:51 UTC
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Frasca-Caccia, Gianluca:
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