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arXiv · 1903.12278

Numerical preservation of multiple local conservation laws

Gianluca Frasca-Caccia·Peter E. Hydon
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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.

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Gianluca Frasca-Caccia, Peter E. Hydon. 2021-10-16. Numerical preservation of multiple local conservation laws. https://arxiv.org/abs/1903.12278

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