Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation

Abstract

This paper presents an effective numerical method for multi-term variable-order time fractional diffusion equations with the variable-order fractional derivative. The local discontinuous Galerkin method and the finite difference method are used in the spatial and temporal directions, respectively. We prove that the scheme is unconditional stable and convergent with O(hs+1+(Δt)2−r), where r=max{ɛ(t)}. s, h, Δt are the degree of piecewise polynomials, the space step sizes, and the time step sizes, respectively. Some numerical experiments are used to illustrate the effectiveness and applicability of the scheme.