三维时间分数阶扩散方程的数值算法  

Numerical Algorithm for Three-dimensional Time-fractional Diffusion Equation

作　　者：赵越 张学莹[1] ZHAO Yue;ZHANG Xueying(College of Science,Hohai University,Jiangsu Nanjing 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《河北师范大学学报（自然科学版）》2018年第5期386-391,共6页Journal of Hebei Normal University：Natural Science

基　　金：教育部留学回国人员科研启动基金(20145003412);江苏省自然科学基金(BK20160853)

摘　　要：将2次插值和Kansa方法结合应用于求解时间分数阶扩散方程,选择多重二次函数(multiquadric,MQ函数)作为径向基函数.在离散过程中,将Kansa方法用于离散空间导数,用线性插值和3点2次插值来近似Caputo型时间分数阶导数.最后讨论了数值算例的数值解,通过实验得出数值解与解析解之间的误差较小、整体稳定性好,从而验证了该方法求解分数阶扩散方程的有效性、可行性和准确性.In this paper,the quadratic interpolation method and the Kansa method are combined to solve the time fractional diffusion equation,in which the multiple quadratic function（referred to as MQ function）is chosen as the radial basis function.In the discrete process,the Kansa method is applied to the discrete space derivative,and the linear interpolation and the cubic point interpolation are applied to approximate the Caputo-type time fractional derivative.Experimental results show that the error between the numerical solution and the analytic solution is small and the overall stability is good.This approach achieves the validity,feasibility and accuracy in solving the time fractional diffusion equation.

关 键 词：分数阶扩散方程 Kansa方法 插值法 径向基函数 

分 类 号：O242.1[理学—计算数学] O302[理学—数学]