A CLASS OF SECOND ORDER DIFFERENCE APPROXIMATIONS FOR SOLVING SPACE FRACTIONAL DIFFUSION EQUATIONS
A CLASS OF SECOND ORDER DIFFERENCE APPROXIMATIONS FOR SOLVING SPACE FRACTIONAL DIFFUSION EQUATIONS
复制标题
求解空间分数扩散方程的一类二阶差分近似
DOI：
10.1090/s0025-5718-2015-02917-2
复制
发表时间：
2015-07-01
影响因子：
2
通讯作者：
Deng, Weihua
中科院分区：
文献类型：
--
作者：
Tian, Wenyi;Zhou, Han;Deng, Weihua
针对Riemann-Liouville分数阶导数，提出了一类二阶近似，称为加权移位格伦瓦尔德差分算子，并将其有效地应用于一维和二维空间分数阶扩散方程的数值求解。从理论上建立了一维和二维常系数空间分数阶扩散方程差分格式的稳定性和收敛性。通过几个算例验证了数值格式的有效性和收敛顺序，并给出了变系数问题的数值结果。
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.