MATH-PHOct 26, 2011
Symmetry Preserving Numerical Schemes for Partial Differential Equations and their Numerical TestsRaphaël Rebelo, Francis Valiquette
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.