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Some Second-Order σ Schemes Combined with an H 1 -Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation

Author

Listed:
  • Yaxin Hou

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Cao Wen

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Hong Li

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Yang Liu

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Zhichao Fang

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Yining Yang

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

Abstract

In this article, some high-order time discrete schemes with an H 1 -Galerkin mixed finite element (MFE) method are studied to numerically solve a nonlinear distributed-order sub-diffusion model. Among the considered techniques, the interpolation approximation combined with second-order σ schemes in time is used to approximate the distributed order derivative. The stability and convergence of the scheme are discussed. Some numerical examples are provided to indicate the feasibility and efficiency of our schemes.

Suggested Citation

  • Yaxin Hou & Cao Wen & Hong Li & Yang Liu & Zhichao Fang & Yining Yang, 2020. "Some Second-Order σ Schemes Combined with an H 1 -Galerkin MFE Method for a Nonlinear Distributed-Order Sub-Diffusion Equation," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:187-:d:316225
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    References listed on IDEAS

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    1. 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).
    2. Yimin Zhao, 2017. "Space as method," City, Taylor & Francis Journals, vol. 21(2), pages 190-206, March.
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