Journal of Applied Mathematics & Bioinformatics

Two implicit finite difference methods for time fractional diffusion equation with source term

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• Abstract

  Time fractional diffusion equation currently attracts attention because it is a useful tool to describe problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order a ∈ (0,1) . In this paper, two different implicit finite difference schemes for solving the time fractional diffusion equation with source term are presented and analyzed, where the fractional derivative is described in the Caputo sense. Numerical experiments illustrate the effectiveness and stability of these two methods respectively. Further, by using the Von Neumann method, the theoretical proof for stability is provided. Finally, a numerical example is given to compare the accuracy of the two mentioned finite difference methods.