A novel finite element method for the distributed-order time fractional Cable equation in two dimensions

摘要

In this paper, the unstructured mesh Galerkin finite element method with a weighted and shifted Grunwald difference approximation and Composite Trapezoid formula is presented to solve the nonhomogeneous two-dimensional distributed order time fractional Cable equation on irregular convex domains. The Crank-Nicolson type discretization of the finite element scheme is implemented to obtain the numerical solution. The stability and convergence of the numerical scheme are discussed and derived. Finally, some numerical examples on irregular convex domains are given to confirm our theoretical results. (C) 2020 Elsevier Ltd. All rights reserved.