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A Spectral Deferred Correction Method for Fractional Differential Equations

Author

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  • Jia Xin
  • Jianfei Huang
  • Weijia Zhao
  • Jiang Zhu

Abstract

A spectral deferred correction method is presented for the initial value problems of fractional differential equations (FDEs) with Caputo derivative. This method is constructed based on the residual function and the error equation deduced from Volterra integral equations equivalent to the FDEs. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDEs without the penalty of a huge computational cost due to the nonlocality of Caputo derivative. Finally, preliminary numerical experiments are given to verify the efficiency and accuracy of this method.

Suggested Citation

  • Jia Xin & Jianfei Huang & Weijia Zhao & Jiang Zhu, 2013. "A Spectral Deferred Correction Method for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:139530
    DOI: 10.1155/2013/139530
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    References listed on IDEAS

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    1. Yuste, S.B & Acedo, L, 2004. "Some exact results for the trapping of subdiffusive particles in one dimension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 334-346.
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