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On the convergence of piecewise polynomial collocation methods for variable-order space-fractional diffusion equations

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  • Yuan, Wenping
  • Liang, Hui
  • Chen, Yanping

Abstract

In this study, we present a piecewise polynomial collocation method for the boundary-value problem of variable-order linear space-fractional diffusion equations. The proposed model is transformed to a weakly singular Volterra integral equation (VIE) of the second kind by an auxiliary variable, then a collocation method is constructed and analyzed for the obtained VIE. We demonstrate the existence and uniqueness of the collocation solution, as well as the optimal convergence order of the collocation method. Some numerical experiments are given to illustrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:209:y:2023:i:c:p:102-117
    DOI: 10.1016/j.matcom.2023.02.013
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    1. 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.
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