%0 Journal Article
%T ON THE ITERATION ALGORITHM FOR AN INVERSE PROBLEM OF PARABOLIC EQUATION<br>一类抛物型方程系数反问题的分裂算法
%A Su Jingxun
%A Liu Jijun
%A <br>苏京勋
%A 刘继军
%J 计算数学
%D 2008
%I 
%X Consider an inverse problem for recovering q(x) in the equation u_t-a~2u_(xx) q(x)u=0, using the final measurement data u(x,T)=Z_T(x).By introducing a function transform v=u_t/u,the solution to this nonlinear ill-posed inverse problem is obtained by two steps. We firstly solve a non-linear direct problem for v(x,t) by iteration algorithm from the inver- sion input data.This procedure is independent of the unknown coefficient q(x).Then the reconstruction of q(x) is finished from a differential relation between v and q approximately. Using this scheme,the original problem is decomposed as a nonlinear well-posed problem and an ill-posed problem.The convergence result is proven.Numerical results are given to show the validity of this decomposition scheme.
%K Inverse problem
%K parabolic equation
%K iteration algorithm
%K sweep method
%K regularization
%K numerics<br>反问题
%K 抛物型方程
%K 迭代方法
%K Sweep方法
%K 正则化
%K 数值解
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=CC77F3CEF526D9CF0B3021650FB4E57E&aid=20F75BB004715FFE3A3681AF2C028505&yid=67289AFF6305E306&vid=340AC2BF8E7AB4FD&iid=CA4FD0336C81A37A&sid=A4FA325EA800C820&eid=59906B3B2830C2C5&journal_id=0254-7791&journal_name=计算数学&referenced_num=0&reference_num=9