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    Differential Quadrature and Cubature Methods for Steady-State Space-Fractional Advection-Diffusion Equations

    Guofei Pang1, Wen Chen1,2, K.Y. Sze3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.4, pp. 299-322, 2014, DOI:10.3970/cmes.2014.097.299

    Abstract Space-fractional advection-diffusion equation is a promising tool to describe the solute anomalous transport in underground water, and it has been extended to multi-dimensions with the help of weighted, fractional directional diffusion operator [Benson, Wheatcraft and Meerschaert (2000)]. Due to the nonlocal property of the space-fractional derivative, it is always a challenge to develop an efficient numerical solution method. The present paper extends the polynomialbased differential quadrature and cubature methods to the solution of steady-state spatial fractional advection-diffusion equations on a rectangular domain. An improved differential cubature method is proposed which accelerates the solution process considerably. Owing to the global interpolation… More >

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