一种基于微分求积的空间分数阶扩散方程求解方法

This article is devoted to develop a direct numerical approach for the space-fractional diffusion equation with variable coefficients by differential quadrature (DQ) technique. Two DQ approximations of fractional derivatives based on Reciprocal Multiquadric and Thin-Plate Spline radial basis functions(RBFs) are introduced and applied to turn the equation in consideration into a set of easily solvable ordinary differential equations, which are discretized by the Crank-Nicolson scheme. The presented methods are verified by five numerical examples and the numerical results illustrate that they outperform some existing algorithms in term of both accuracy and efficiency as long as the shape parameters of RBFs are properly chosen.