Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 94, Issue 6, Pages 1172-1184Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2016.1184262
Keywords
Fractional diffusion equation; spectral method; Legendre polynomials; fractional trapezoid formula; unified numerical method; 45D05; 65M06; 65M12; 65M70
Categories
Funding
- National Natural Science Foundation of China [11426141]
- Jiangsu Overseas Research or Training Program for University Prominent Young Faculty and Presidents
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In this paper we develop a unified difference-spectral method for stably solving time-space fractional sub-diffusion and super-diffusion equations. Based on the equivalence between Volterra integral equations and fractional ordinary differential equations with initial conditions, this proposed method is constructed by combining the spectral Galerkin method in space and the fractional trapezoid formula in time. Numerical experiments are carried out to verify the effectiveness of the method, and demonstrate that the unified method can achieve spectral accuracy in space and second-order accuracy in time for solving two kinds of time-space fractional diffusion equations.
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