Alternating direction implicit difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel

摘要

We present an alternating direction implicit (ADI) difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel. The Caputo fractional derivative is discretized by L1 method and the integro-differential term is discretized by a convolution quadrature suggested by Lubich. The stability and optimal convergence order estimate of the difference scheme are derived. Numerical experiments verify our theory analysis. (C) 2019 Elsevier Ltd. All rights reserved.