Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem  

作　　者：Xingyang Ye Chuanju Xu 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,Fujian,China [2]School of Science,Jimei University,Xiamen 361021,Fujian,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2013年第3期499-519,共21页高等学校计算数学学报（英文版）

基　　金：The work of X.Y was partially supported by the Natural Science Foundation of Fujian Province,China(Grant No.2012J01013);The work of C.X.was partially supported by National NSF of China(Grants 11071203 and 91130002).

摘　　要：An inverse problem of reconstructing the initial condition for a time fractional diffusion equation is investigated.On the basis of the optimal control framework,the uniqueness and first order necessary optimality condition of the minimizer for the objective functional are established,and a time-space spectral method is proposed to numerically solve the resulting minimization problem.The contribution of the paper is threefold:1)a priori error estimate for the spectral approximation is derived;2)a conjugate gradient optimization algorithm is designed to efficiently solve the inverse problem;3)some numerical experiments are carried out to show that the proposed method is capable to find out the optimal initial condition,and that the convergence rate of the method is exponential if the optimal initial condition is smooth.

关 键 词：Time fractional diffusion equation inverse problem spectral method error estimate conjugate gradient method. 

分 类 号：O17[理学—数学]