时间分数阶扩散方程柯西问题的迭代正则化方法  

Iterative Regularization Method for the Cauchy Problem of Time-Fractional Diffusion Equation

作　　者：吕拥 张宏武 LV Yong;ZHANG Hongwu(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《应用数学》2023年第4期1007-1024,共18页Mathematica Applicata

基　　金：Supported by the NSF of Ningxia(2022AAC03234);the NSF of China(11761004);the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09);the Postgraduate Innovation Project of North Minzu University(YCX22094)。

摘　　要：本文研究一类时间分数阶扩散方程柯西问题,该问题是严重不适定的.基于傅里叶截断理论,构造了一种迭代方法来克服其不适定性,并且通过正则化参数的先验和后验选取规则获得了正则化方法的收敛性估计.最后,通过数值实验验证了该方法的有效性.数值结果表明,该方法求解时间分数阶扩散方程柯西问题是稳定可行的.We consider a Cauchy problem of the time-fractional diffusion equation,which is seriously ill-posed.This paper constructs an iterative regularization method based on Fourier truncation to overcome the ill-posedness of considered problem.And then,under the a-prior and a-posterior selection rules of regularization parameter,the convergence estimates of the proposed method are derived.Finally,we verify the effectiveness of our method by doing some numerical experiments.The corresponding numerical results show that the proposed method is stable and feasible in solving the Cauchy problem of time-fractional diffusion equation.

关 键 词：柯西问题 时间分数阶扩散问题 迭代正则化方法 收敛性估计 数值模拟 

分 类 号：O175.24[理学—数学] O175.26[理学—基础数学]