SOLUTION OF BACKWARD HEAT PROBLEM BY MOROZOV DISCREPANCY PRINCIPLE AND CONDITIONAL STABILITY  

作　　者：李徽 刘继军 

机构地区：[1]Department of Mathematics, Southeast University, Nanjing 210096, PRC.

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》2005年第2期180-192,共13页

基　　金：This work is supported by NSFC(No．10371018).

摘　　要：Consider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, to) for to ∈ (0, T) from the measured data u(x, T)respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversionConsider a 1-D backward heat conduction problem with Robin boundary condition. We recover u(x, 0) and u(x, t0) for to ∈(0, T) from the measured data u(x, T) respectively. The first problem is solved by the Morozov discrepancy principle for which a 3-order iteration procedure is applied to determine the regularizing parameter. For the second one, we combine the conditional stability with the Tikhonov regularization together to construct the regularizing solution for which the convergence rate is also established. Numerical results are given to show the validity of our inversion method

关 键 词：后向热问题 正则化 条件稳定性 收敛性 罗宾边界条件 

分 类 号：O241[理学—计算数学]