Journal of Guangdong University of Technology ›› 2019, Vol. 36 ›› Issue (03): 74-79.doi: 10.12052/gdutxb.180122

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Finite Difference Schemes for Time Fractional Diffusion Equations with Periodic Boundary Conditions

Zhang Hui-qin, Wang Zhi-bo   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2018-09-20 Online:2019-05-09 Published:2019-04-04

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Abstract: Generally, the analytic solution for fractional differential equations is hard to obtain. The difference scheme of time fractional diffusion equations with periodic boundaries is mainly studied, adopting the L2-1σ formula in temporal direction, and the second order difference approximation in spatial direction. The proposed scheme can obtain second order accuracy globally. The unique solvability, stability and convergence of the proposed scheme are proved by the Fourier method. Finally, the specific fractional models are solved numerically by MATLAB language. Numerical experiments are carried out to support the theoretical results.

Key words: fractional diffusion equation, Fourier method, variable coefficients, stability, convergence

CLC Number: 

  • 35R11
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