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Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation

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Abstract

The objective of this paper is to find the numerical solution of two-dimensional multi-term time fractional mobile-immobile equation. The proposed technique is based on the arbitrary-order orthogonal spline collocation method for the spatial discretization, the L1 approximation for the Caputo fractional derivative, and a second-order backward differentiation formula in time. The stability and convergence are proved in detail. Then, the convergence analysis is validated by a number of numerical experiments.

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Acknowledgements

The authors would like to thank the editor and reviewers for their constructive comments and suggestions, which helped the authors to improve the quality of the paper significantly. This research was partly supported by the National Natural Science Foundation of China (No. 12101080, 11701103), Young Top-notch Talent Program of Guangdong Province (No. 2017GC010379), Natural Science Foundation of Guangdong Province (No. 2019A1515010876), the Project of Science and Technology of Guangzhou (No. 201904010341, 202102020704), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (2021023), and the Project of Department of Education of Guangdong Province (No. 2017KTSCX062).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

    Zhibo Wang

  2. College of Mathematics Statistics, Changsha University of Science and Technology, Changsha, 410114, Hunan, China

    Leijie Qiao

  3. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China

    Da Xu

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  1. Leijie Qiao
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  2. Da Xu
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  3. Zhibo Wang
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Correspondence to Zhibo Wang.

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Qiao, L., Xu, D. & Wang, Z. Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation. J. Appl. Math. Comput. 68, 3199–3217 (2022). https://doi.org/10.1007/s12190-021-01661-3

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  • DOI: https://doi.org/10.1007/s12190-021-01661-3

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