Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:290

Article

Dehghan, Mehdi¹  Safarpoor, Mansour¹  Abbaszadeh, Mostafa¹ 

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran

关键词: Multi-term time fractional diffusion-wave equations;    High order compact finite difference;    Galerkin spectral method;    Solvability;    Energy method;    Convergence and stability;   

DOI  :  10.1016/j.cam.2015.04.037

来源: Elsevier

【 摘 要 】

In this paper we apply a high order difference scheme and Galerkin spectral technique for the numerical solution of multi-term time fractional partial differential equations. The proposed methods are based on a finite difference scheme in time. The time fractional derivatives which have been described in Caputo's sense are approximated by a scheme of order 0(tau(3-a)), 1 < alpha < 2 and the space derivative is discretized with a fourth-order compact finite difference procedure and Galerkin spectral method. We prove the unconditional stability of the compact procedure by coefficient matrix property. The L-infinity-convergence of the compact finite difference method has been proved by the energy method. Also we obtain an error estimate for Galerkin spectral method. Numerical results are provided to verify the accuracy and efficiency of the proposed schemes. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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