A modified method for a non-standard inverse heat conduction problem

Applied Mathematics and Computation

Volumn 180, Issue 2, 2006, Pages 453-468

  Qian, Zhi ^a   Fu, Chu Li ^a   Xiong, Xiang Tuan ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Error estimate; Ill posed problem; Inverse heat conduction; Regularization

Indexed keywords

DATA REDUCTION; ERROR ANALYSIS; INVERSE PROBLEMS; NUMERICAL METHODS; PROBLEM SOLVING;

ERROR ESTIMATES; ILL-POSED PROBLEMS; INVERSE HEAT CONDUCTION; REGULARIZATION;

HEAT CONDUCTION;

EID: 33748967948     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.12.033     Document Type: Article

References (18)

1. Hào D.N., and Reinhardt H.-J. On a sideways parabolic equation. Inverse Problems 13 (1997) 297-309
2. Qiu C.Y., and Fu C.L. Wavelet regularization for an ill-posed problem of parabolic equation. Acta Math. Sci. 22A 3 (2002) 361-372
3. Beck J.V. Nonlinear estimation applied to the nonlinear inverse heat conduction problem. Int. J. Heat Mass Transfer 13 (1970) 703-716
4. Xiong X.T., Fu C.L., and Li H.F. Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem. Appl. Math. Comput. 157 1 (2004) 77-91
5. Cannon J.R. The One-Dimensional Heat Equation (1984), Addison-Wesley, Reading, MA
6. Lavrent'ev M.M., Romanov V.G., and Shishatskii S.P. Ill-posed Problems of Mathematical Physics and Analysis (1986), AMS, Providence, RI
7. Tikhonov A.N., and Arsenin V.Y. Solutions of Ill-posed Problems (1977), John Wiley & Sons, New York
8. Engl H.W., Hanke M., and Neubauer A. Regularization of Inverse Problems (1996), Kluwer Academic, Boston, MA
9. Kirsch A. An Introduction to the Mathematical Theory of Inverse Problems (1999), Springer-Verlag, Berlin
10. Fu C.-L., Li H.-F., Xiong X.-T., and Fu P. Optimal Tikhonov approximation for a sideways parabolic equation. Int. J. Math. Math. Sci. 8 (2005) 1221-1237
11. Eldén L., Berntsson F., and Regiǹska T. Wavelet and Fourier methods for solving the sideways heat equation. SIAM J. Sci. Comput. 21 6 (2000) 2187-2205
12. Hào D.N., Reinhardt H.-J., and Schneider A. Numerical solution to a sideways parabolic equation. Int. J. Numer. Meth. Eng. 50 (2001) 1253-1267
13. Eldén L. Approximations for a Cauchy problem for the heat equation. Inverse Problems 3 (1987) 263-273
14. Eldén L. Solving an inverse heat conduction problem by 'Method of lines'. Trans. ASME J. Heat Transfer 119 (1997) 913-923
15. Eldén L. Numerical solution of the sideways heat equation by difference approximation in time. Inverse Problems 11 (1995) 913-923
16. Z. Qian, C.L. Fu, X.T. Xiong, Fourth-order modified method for the Cauchy problem for the Laplace equation, J. Comput. Appl. Math., in press.
17. Gustafsson B., Kreiss H.-O., and Oliger J. Time Dependent Problems and Difference Methods (1995), Wiley Interscience, New York
18. Lambert J.D. Numerical Methods for Ordinary Differential Systems (1991), Wiley, New York