The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Numerical analysis

摘要

In this article, three kinds of typical Caputo-type partial differential equations are numerically studied via the finite difference methods/the local discontinuous Galerkin finite element methods, including Caputo-type reaction-diffusion equation, Caputo-type reaction-diffusion-wave equation, and Caputo-type cable equation. The derived numerical schemes are unconditionally stable and convergent. The numerical experiments are also displayed which support the theoretical analysis. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.