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- W2891623556 abstract "Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures with different scales. Extending the discretizations for fractional substantial calculus [Chen and Deng, emph{ ESAIM: M2AN.} textbf{49}, (2015), 373--394], we first provide the numerical discretizations of the Caputo-Fabrizio fractional derivative with the global truncation error $mathcal{O}(tau^nu)$ $ (nu=1,2,3,4)$. Then we use the derived schemes to solve the Caputo-Fabrizio fractional diffusion equation. By analysing the positive definiteness of the stiffness matrices of the discretized Caputo-Fabrizio operator, the unconditional stability and the convergence with the global truncation error $mathcal{O}(tau^2+h^2)$ are theoretically proved and numerical verified." @default.
- W2891623556 created "2018-09-27" @default.
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- W2891623556 date "2018-09-10" @default.
- W2891623556 modified "2023-09-23" @default.
- W2891623556 title "High order algorithms for Fokker-Planck equation with Caputo-Fabrizio fractional derivative" @default.
- W2891623556 doi "https://doi.org/10.48550/arxiv.1809.03263" @default.
- W2891623556 hasPublicationYear "2018" @default.
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