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Simple bespoke preservation of two conservation laws

Frasca-Caccia, Gianluca, Hydon, Peter E. (2018) Simple bespoke preservation of two conservation laws. IMA Journal of Numerical Analysis, 40 (2). pp. 1294-1329. ISSN 0272-4979. E-ISSN 1464-3642. (doi:10.1093/imanum/dry087) (KAR id:70284)


Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of the Euler operator, an observation that was first used recently to construct approximations symbolically that preserve two conservation laws of a given PDE. However, the complexity of the symbolic computations has limited the effectiveness of this approach. The current paper introduces some key simplifications that make the symbolic-numeric approach feasible. To illustrate the simplified approach, we derive bespoke finite difference schemes that preserve two discrete conservation laws for the Korteweg-de Vries (KdV) equation and for a nonlinear heat equation. Numerical tests show that these schemes are robust and highly accurate compared to others in the literature.

Item Type: Article
DOI/Identification number: 10.1093/imanum/dry087
Uncontrolled keywords: Finite difference methods; discrete conservation laws; KdV equation; nonlinear heat equation;porous medium equation.
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Hydon
Date Deposited: 22 Nov 2018 16:23 UTC
Last Modified: 09 Dec 2022 07:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

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