Iteration methods on sideways parabolic equations

作者：Deng, Youjun^*; Liu, Zhenhai

来源：Inverse Problems, 2009, 25(9): 095004.

DOI：10.1088/0266-5611/25/9/095004

• discrepancy
• principle
• selection

We consider an inverse heat conduction problem (IHCP) in the quarter plane, where data are given at x = 1. The problem is called a sideways parabolic equation and is severely ill-posed. Numerical methods such as Tikhonov and Fourier regularization methods have been developed. However, they contain an a priori bound of the solution in their parameter choice. A large estimate bound may cause bad numerical results. In this paper, we introduce a new class of iteration methods to solve the IHCP and prove that our methods are of order optimal under both a priori and a posteriori stopping rules. An appropriate selection of a parameter in the iteration scheme helps to reduce the iterative steps and get a satisfactory approximate solution. Furthermore, if we use the discrepancy principle, we can avoid the selection of the a priori bound.

• 出版日期2009-9
• 单位中南大学