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Moving collocation methods for time fractional differential equations and simulation of blowup

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Abstract

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.

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Authors and Affiliations

  1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China

    JingTang Ma

  2. Department of Mathematics and Scientific Computing, Changsha University of Science and Technology, Changsha, 410076, China

    YingJun Jiang

Authors
  1. JingTang Ma
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  2. YingJun Jiang
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Correspondence to JingTang Ma.

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Ma, J., Jiang, Y. Moving collocation methods for time fractional differential equations and simulation of blowup. Sci. China Math. 54, 611–622 (2011). https://doi.org/10.1007/s11425-010-4133-1

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  • DOI: https://doi.org/10.1007/s11425-010-4133-1

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