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An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

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  • Lei Ren
  • Lei Liu

Abstract

In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the - approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.

Suggested Citation

  • Lei Ren & Lei Liu, 2019. "An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-9, August.
    • Handle: RePEc:hin:jnlamp:3263589
    DOI: 10.1155/2019/3263589
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