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

For researchers in numerical PDEs, this work provides a method to construct discretizations that preserve symmetries, leading to improved accuracy, though the approach is incremental as it applies existing theory to new equations.

The authors developed symmetry-preserving finite difference schemes for PDEs using equivariant moving frames, and showed via numerical tests that these invariant schemes achieve higher accuracy than standard discretizations on uniform rectangular meshes for the heat equation with a logarithmic source and the spherical Burgers equation.