Abstract
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.
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