A unified difference-spectral method for time-space fractional diffusion equations

作者：Huang, Jianfei; Yang, Dandan^*

来源：International Journal of Computer Mathematics, 2017, 94(6): 1172-1184.

DOI：10.1080/00207160.2016.1184262

• Fractional diffusion equation
• spectral method
• Legendre polynomials
• fractional trapezoid formula
• unified numerical method
• 45D05
• 65M06
• 65M12
• 65M70

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.

• 出版日期2017
• 单位青岛大学; 淮阴师范学院