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Error estimates of a spectral Petrov–Galerkin method for two-sided fractional reaction–diffusion equations

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  • Hao, Zhaopeng
  • Lin, Guang
  • Zhang, Zhongqiang

Abstract

We study regularity and the spectral method for two-sided fractional diffusion equations with a reaction term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard Sobolev spaces. With this regularity, we prove an optimal error estimate for the spectral Petrov–Galerkin method. Numerical results are presented to verify our theoretical convergence orders.

Suggested Citation

  • Hao, Zhaopeng & Lin, Guang & Zhang, Zhongqiang, 2020. "Error estimates of a spectral Petrov–Galerkin method for two-sided fractional reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s009630032030014x
    DOI: 10.1016/j.amc.2020.125045
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    References listed on IDEAS

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    1. Yimin Zhao, 2017. "Space as method," City, Taylor & Francis Journals, vol. 21(2), pages 190-206, March.
    2. Yin, Baoli & Liu, Yang & Li, Hong, 2020. "A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations," Applied Mathematics and Computation, Elsevier, vol. 368(C).
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