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An Efficient Numerical Algorithm for the Model Describing the Competition Between Super- and Sub-diffusions Driven by Fractional Brownian Sheet Noise

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Abstract

Super- and sub-diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub-diffusions driven by fractional Brownian sheet noise. Based on the obtained regularization result of the solution by using the properties of Mittag–Leffler function and the regularized noise by Wong–Zakai approximation, we make full use of the regularity of the solution operators to achieve optimal convergence of the regularized solution. The spectral Galerkin method and the Mittag–Leffler Euler integrator are respectively used to deal with the space and time operators. In particular, by contour integral, the fast evaluation of the Mittag–Leffler Euler integrator is realized. We provide complete error analyses, which are verified by the numerical experiments.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant Nos. 12071195, 12201270, and 12225107, the Innovative Groups of Basic Research in Gansu Province under Grant No. 22JR5RA391, the science and technology plan of Gansu Province under Grant No. 22JR5RA535, the Fundamental Research Funds for the Central Universities under Grant No. lzujbky-2022-pd04, and China Postdoctoral Science Foundation under Grant No. 2022M721439.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Jing Sun, Daxin Nie & Weihua Deng

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  1. Jing Sun
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  2. Daxin Nie
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  3. Weihua Deng
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Correspondence to Weihua Deng.

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Sun, J., Nie, D. & Deng, W. An Efficient Numerical Algorithm for the Model Describing the Competition Between Super- and Sub-diffusions Driven by Fractional Brownian Sheet Noise. J Sci Comput 96, 10 (2023). https://doi.org/10.1007/s10915-023-02240-3

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