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Finite difference scheme for the time-space fractional diffusion equations

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Central European Journal of Physics

Abstract

In this paper, we derive two novel finite difference schemes for two types of time-space fractional diffusion equations by adopting weighted and shifted Grünwald operator, which is used to approximate the Riemann-Liouville fractional derivative to the second order accuracy. The stability and convergence of the schemes are analyzed via mathematical induction. Moreover, the illustrative numerical examples are carried out to verify the accuracy and effectiveness of the schemes.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Jianxiong Cao & Changpin Li

Authors
  1. Jianxiong Cao
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  2. Changpin Li
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Correspondence to Changpin Li.

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Cao, J., Li, C. Finite difference scheme for the time-space fractional diffusion equations. centr.eur.j.phys. 11, 1440–1456 (2013). https://doi.org/10.2478/s11534-013-0261-x

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  • DOI: https://doi.org/10.2478/s11534-013-0261-x

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