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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 2 − α 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 L2‐1σ 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, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:3263589
    DOI: 10.1155/2019/3263589
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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