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. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.