近似特别解法解变时间分数阶扩散方程  

METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR VARIABLE-ORDER FRACTIONAL DIFFUSION MODELS

作　　者：刘荟[1] 张学莹[1] 

机构地区：[1]河海大学理学院,南京211100

出　　处：《山东师范大学学报（自然科学版）》2016年第3期37-42,共6页Journal of Shandong Normal University(Natural Science)

摘　　要：近似特别解(MAPS)是一种基于径向基函数(RBFs)插值的无网格方法.本文采用近似特别解法来解决变时间分数阶扩散方程,在离散过程中,用有限差分法离散时间分数阶导数,用近似特别解法离散扩散项,选择薄板样条函数作为径向基函数,并把所得结果和MQ插值函数进行对比.数值结果表明在解决变时间分数阶扩散方程时,薄板样条函数所得结果比MQ函数结果更稳定,同时避免了形参c的选择,且有较高的精度和计算效率.The method of approximate solutions （MAPS） is a meshless method which is based on radial basic functions interpolation. We apply the MAPS to solve variable- order time fractional diffusion models. In the discretization formulation, a finite difference scheme discretizes time fractional derivative and MAPS discretizes spatial derivative terms respectively. We choose the thin plate spline function as RBFs and compare it with the MQ functions. The numerical results show that the results obtained by the thin plate spline function are more stable than the MQ function in solving variable-order time fractional diffusion equation. Selecting the thin plate spline function can avoid choosing shape parameter and has higher accuracy and computational efficiency.

关 键 词：近似特别解 径向基函数 变时间分数阶扩散方程 

分 类 号：O242.1[理学—计算数学] O302[理学—数学]