插值法解时间分数阶扩散方程  

Interpolation method for the time fractional diffusion equation

作　　者：闵宝峰 张学莹[1] MIN Baofeng;ZHANG Xueying(College of Science, Hohai University, Nanjing 211100, Jiangsu, China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《陕西师范大学学报（自然科学版）》2018年第3期55-59,共5页Journal of Shaanxi Normal University：Natural Science Edition

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：针对一类时间分数阶扩散方程提出了一种新的隐式差分格式,空间导数直接采用中心差分格式离散,为了近似Caputo型时间分数阶导数,在小区间[t_(n-1),t_n](2≤n≤N)上使用三点u(x,t_(n-2))、u(x,t_(n-1))、u(x,t_n)二次插值近似u(x,t)的值,在小区间[t_0,t_1]上使用线性插值近似u(x,t)的值,并利用能量范数证明该格式的无条件稳定性和收敛性,最后通过数值实验验证该格式的有效性。A new implicit difference approximation to solve a time fractional derivative equation is proposed. The spatial derivative is directly discretized by central difference scheme. To approxi- mate the Caputo fractional derivative, it is established by means of the quadratic interpolation approximation. Using three points U（X,tn-2）,U（X,tn-1）,U（X,tn） for the integrand u（x,t） on each small interval [tn-1,tn]（2≤n≤N）, while the linear interpolation approximation is applied on the first small interval [t0 ,tl]. Using the energy norm, the unconditional stability and convergence of the scheme are proved. Finally, a numerical experiment shows that the scheme is efficient.

关 键 词：时间分数阶扩散方程 隐式差分格式 稳定性 收敛性 

分 类 号：O242.1[理学—计算数学] O302[理学—数学]