A unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Chen, Hu¹  Lu, Shujuan¹  Chen, Wenping¹ 

[1] Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China

关键词: Fractional diffusion equation;    Fractional diffusion-wave equation;    Spectral method;    Stability;    Convergence;   

DOI  :  10.1016/j.cam.2017.09.011

来源: Elsevier

【 摘 要 】

We consider the numerical solutions of the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients in a bounded domain. The time fractional derivatives are described in the Caputo sense. A unified numerical scheme based on finite difference method in time and Legendre spectral method in space is proposed. Detailed error analysis is given for the fully discrete scheme. The convergence rate of the proposed scheme in L-2 norm is O(tau(2) + N1-m), where tau, N, and m are the time-step size, polynomial degree, and regularity in the space variable of the exact solution, respectively. Numerical examples are presented to illustrate the theoretical results. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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