Boundary Value Problems
Volume 2009 (2009), Article ID 260941, 13 pages
doi:10.1155/2009/260941
Research Article

Solving the Axisymmetric Inverse Heat Conduction Problem by a Wavelet Dual Least Squares Method

Wei Cheng1 and Chu-Li Fu2

1College of Science, Henan University of Technology, Zhengzhou 450001, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received 17 August 2008; Revised 23 January 2009; Accepted 10 March 2009

Academic Editor: Ugur Abdulla

Copyright © 2009 Wei Cheng and Chu-Li Fu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution (if it exists) does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order optimal error estimate between the approximate solution and exact solution is proved.