Numerical methods for solving the Robin boundary value problem for a generalized diffusion equation with a non-smooth solution

Abstract

Solutions of Robin boundary value problem for a generalized diffusion equation with a non-smooth solution are studied. The Caputo derivative in the generalized sense has been discretized by using a difference scheme of order (2 - α) on a non-uniform mesh with 0 < α< 1 in the temporal direction. Test example shows how the grading of the mesh is essential for non-smooth solution and using such kind of mesh generate stronger results.