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

2011/10/26 by Raphaël Rebelo, Rebelo, Raphaël, Francis Valiquette +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #58J70 #68N06 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1110.5921

openalex publication_date 2011/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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