应用数学2023，Vol.36Issue(4)：1007-1024,18.
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
摘要
Abstract
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Key words
Cauchy problem/Time-fractional diffusion equation/Iteration regularization method/Convergence estimate/Numerical simulation分类
数理科学引用本文复制引用
吕拥,张宏武..时间分数阶扩散方程柯西问题的迭代正则化方法[J].应用数学,2023,36(4):1007-1024,18.基金项目
Supported by the NSF of Ningxia(2022AAC03234),the NSF of China(11761004),the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)and the Postgraduate Innovation Project of North Minzu University(YCX22094) （2022AAC03234）
