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arXiv · 2209.01295

Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise

Jing Sun·Daxin Nie·Weihua Deng
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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 regulization 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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Jing Sun, Daxin Nie, Weihua Deng. 2022-09-02. Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise. https://arxiv.org/abs/2209.01295

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