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A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations

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  • Lin Zhu

Abstract

Using the asymmetric discretization technique, an explicit finite difference scheme is constructed for one-dimensional spatial fractional diffusion equations (FDEs). The spatial fractional derivative is approximated by the weighted and shifted Grünwald difference operator. The scheme can be solved explicitly by calculating unknowns in the different nodal-point sequences at the odd time-step and the even time-step. The uniform stability is proven and the error between the discrete solution and analytical solution is theoretically estimated. Numerical examples are given to verify theoretical analysis.

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  • Lin Zhu, 2019. "A Second-Order Uniformly Stable Explicit Asymmetric Discretization Method for One-Dimensional Fractional Diffusion Equations," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    • Handle: RePEc:hin:complx:4238420
    DOI: 10.1155/2019/4238420
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    1. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    2. Jhinga, Aman & Daftardar-Gejji, Varsha, 2018. "A new finite-difference predictor-corrector method for fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 418-432.
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