Fourth-order modified method for the Cauchy problem for the Laplace equation

Journal of Computational and Applied Mathematics

Volumn 192, Issue 2, 2006, Pages 205-218

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

^a LANZHOU UNIVERSITY   (China)

Author keywords

Cauchy problem for Laplace equation; Ill posed problem; Regularization

Indexed keywords

APPROXIMATION THEORY; DATA REDUCTION; ERROR ANALYSIS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

CAUCHY PROBLEM FOR LAPLACE EQUATION; ILL-POSED PROBLEM; REGULARIZATION;

LAPLACE TRANSFORMS;

EID: 33646082980     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.04.031     Document Type: Article

References (18)

1. Beck J.V., Blackwell B., and Clair S.R. Inverse Heat Conduction Ill-Posed Problem (1985), Wiley, New York
2. Berntsson F., and Elden L. Numerical solution of a Cauchy problem for the Laplace equation. Inverse Problems 17 (2001) 839-853
3. Chang J.R., Yeih W.C., and Shieh M.H. On the modified Tikhonov's regularization method for the cauchy problem of the Laplace equation. J. Marine Sci. Tech. 9 (2001) 113-121
4. Eldén L. Approximations for a Cauchy problem for the heat equation. Inverse Problems 3 (1987) 263-273
5. Eldén L. Solving an inverse heat conduction problem by 'Method of lines'. Trans. ASME J. Heat Transfer 119 (1997) 913-923
6. Engl H.W., Hanke M., and Neubauer A. Regularization of Inverse Problems (1996), Kluwer Academic, Boston, MA
7. Gustafsson B., Kreiss H.-O., and Oliger J. Time Dependent Problems and Difference Methods (1995), Wiley, New York
8. Hao D.N., and Hien P.M. Stability results for the Cauchy problem for the Laplace equation in a strip. Inverse Problems 19 (2003) 833-844
9. Hao D.N., and Lesnic D. Cauchy problem for Laplace's equation via the conjugate gradient method. IMA J. Appl. Math. 65 (2000) 199-217
10. Kirsch A. An Introduction to the Mathematical Theory of Inverse Problems (1999), Springer, Berlin
11. Lambert J.D. Numerical Methods for Ordinary Differential Systems (1991), Wiley, New York
12. Lavrent'ev M.M., Romanov V.G., and Shishatskii S.P. Ill-posed Problems of Mathematical Physics and Analysis (1986), AMS, Providence, RI
13. Lesnic D., Elliott L., and Ingham D.B. Iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation. Engrg. Anal. Boundary Elements 20 (1997) 123-133
14. Regińska T. Sideways heat equation and wavelets. J. Comput. Appl. Math. 63 (1995) 209-214
15. Tautenhahn U. Optimal stable solution of Cauchy problem for elliptic equations. J. Anal. Appl. 15 (1996) 961-984
16. Tikhonov A.N., and Arsenin V.Y. Solutions of Ill-posed Problems (1977), Wiley, New York
17. Vani C., and Avudainayagam A. Regularized solution of the Cauchy problem for the Laplace equation using Meyer Wavelets. Math. Comput. Model. 36 (2002) 1151-1159
18. Weber C.F. Analysis and solution of the ill-posed inverse conduction problem. Int. J. Heat Mass Transfer 24 (1981) 1783-1792