A CLASS OF SECOND ORDER DIFFERENCE APPROXIMATIONS FOR SOLVING SPACE FRACTIONAL DIFFUSION EQUATIONS

作者：Tian, Wenyi; Zhou, Han; Deng, Weihua

来源：Mathematics of Computation, 2015, 84(294): 1703-1727.

DOI：10.1090/S0025-5718-2015-02917-2

• Riemann-Liouville fractional derivative
• Fractional diffusion equation
• Weighted and shifted Grunwald difference (WSGD) operator

A class of second order approximations, called the weighted and shifted Grunwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions. The stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established. Several numerical examples are implemented to test the efficiency of the numerical schemes and confirm the convergence order, and the numerical results for variable coefficients problem are also presented.

• 出版日期2015-7
• 单位兰州大学