A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
The authors derive a new finite volume scheme for two-sided fractional diffusion equations with Riemann-Liouville derivatives in one spatial dimension. Spatial mesh is non-uniform. The discretisation uses the integral definition of the fractional derivatives. The scheme leads to a diagonally dominant matrix representation and it is proved to be stable and fully conservative. Some numerical examples are presented to justify that the scheme is more accurate for the same number of nodes compared to a uniform mesh.
diagonally dominant matrix representation
scientific article; zbMATH DE number 6818418
scientific article