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arXiv · 1110.5921

Symmetry Preserving Numerical Schemes for Partial Differential Equations and their Numerical Tests

Raphaël Rebelo·Francis Valiquette
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Abstract

The method of equivariant moving frames on multi-space is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for a heat equation with a logarithmic source and the spherical Burgers equation are obtained. Numerical tests show how invariant schemes can be more accurate than standard discretizations on uniform rectangular meshes.

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Raphaël Rebelo, Francis Valiquette. 2011-10-26. Symmetry Preserving Numerical Schemes for Partial Differential Equations and their Numerical Tests. https://arxiv.org/abs/1110.5921

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