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Numerical approximation for a nonlinear variable-order fractional differential equation via a collocation method

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  • Zheng, Xiangcheng

Abstract

We study a numerical approximation for a nonlinear variable-order fractional differential equation via a collocation method. Due to the lack of monotonicity of the discretization coefficients of the variable-order fractional derivative in standard approximation schemes, existing numerical analysis techniques do not apply directly. By an approximate inversion technique, the proposed model is transformed as a second kind Volterra integral equation, based on which a collocation method under uniform or graded mesh is developed and analyzed. In particular, the mesh grading parameter we used is consistent with respect to the regularity of the solutions, and the convergence rates are characterized in terms of the initial value of the variable order, which serve as improvements compared with the existing results in the literature.

Suggested Citation

  • Zheng, Xiangcheng, 2022. "Numerical approximation for a nonlinear variable-order fractional differential equation via a collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 107-118.
    • Handle: RePEc:eee:matcom:v:195:y:2022:i:c:p:107-118
    DOI: 10.1016/j.matcom.2022.01.005
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    Cited by:

    1. Yuan, Wenping & Liang, Hui & Chen, Yanping, 2023. "On the convergence of piecewise polynomial collocation methods for variable-order space-fractional diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 102-117.

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