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Fast numerical approximation for the space-fractional semilinear parabolic equations on surfaces

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Abstract

In this work, a fast numerical method is considered to solve the space-fractional semilinear parabolic equations on closed surfaces. It is a challenge in that how to define the space fractional operator and corresponding semilinear parabolic equation with the energy functional defined on surface. To overcome it, using the local tangential space, we construct the spectral approximation for the space fractional operator on surfaces and apply the matrix transfer technique to avoid the difficulty of fractional nonlocality. The main advantage of the matrix transfer method is the completed diagonal representation of fractional operators from eigenvalue decomposition. Moreover, the time-discrete error estimates are presented as well as the energy stability. Various numerical examples are carried out to verify the theoretical results.

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Acknowledgements

This work is in part supported by the Natural Science Foundation of Xinjiang Province (no. 2016D01C071, no. 2016D01C058) and the NSF of China (nos. 11671345,11861054).

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Xinjiang University, Ürümqi, 830046, People’s Republic of China

    Yuanyang Qiao & Xinlong Feng

  2. College of Mathematics and Statistics, Guangxi Normal University, Guilin, 541006, People’s Republic of China

    Lingzhi Qian

  3. Department of Mathematics, College of Sciences, Shihezi University, Shihezi, 832003, People’s Republic of China

    Lingzhi Qian

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  1. Yuanyang Qiao
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  2. Lingzhi Qian
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  3. Xinlong Feng
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Correspondence to Yuanyang Qiao or Lingzhi Qian.

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Qiao, Y., Qian, L. & Feng, X. Fast numerical approximation for the space-fractional semilinear parabolic equations on surfaces. Engineering with Computers 38 (Suppl 3), 1939–1953 (2022). https://doi.org/10.1007/s00366-021-01357-z

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  • DOI: https://doi.org/10.1007/s00366-021-01357-z

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