A modified method for a backward heat conduction problem

Applied Mathematics and Computation

Volumn 185, Issue 1, 2007, Pages 564-573

  Qian, Zhi ^a   Fu, Chu Li ^a   Shi, Rui ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Backward heat conduction; Ill posedness; Modified method; Regularization

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; ERROR ANALYSIS; HEAT CONDUCTION;

BACKWARD HEAT CONDUCTION; ILL-POSEDNESS; MODIFIED METHODS; REGULARIZATION;

PROBLEM SOLVING;

EID: 33846939256     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.07.055     Document Type: Article

References (16)

1. Hào D.N. A mollification method for ill-posed problems. Numer. Math. 68 (1994) 469-506
2. Payne L.E. Improperly posed problems in partial differential equations. Regional Conference Series in Applied Mathematics (1975), SIAM, Philadelphia, PA
3. Hadamard J. Lectures on Cauchy Problem in Linear Partial Differential Equations (1923), Yale University Press, New Haven, CT
4. Kirsch A. An Introduction to the Mathematical Theory of Inverse Problems (1999), Springer-Verlag, Berlin
5. Lesnic D., Elliott L., and Ingham D.B. An iterative boundary element method for solving the backward heat conduction problem using an elliptic approximation. Inverse Probl. Eng. 6 (1998) 255-279
6. Han H., Ingham D.B., and Yuan Y. The boundary element method for the solution of the backward heat conduction equation. J. Comput. Phys. 116 (1995) 292-299
7. Mera N.S., Elliott L., Ingham D.B., and Lesnic D. An iterative boundary element method for solving the one dimensional backward heat conduction problem. Int. J. Heat Mass Transfer 44 (2001) 1937-1946
8. Mera N.S., Elliott L., and Ingham D.B. An inversion method with decreasing regularization for the backward heat conduction problem. Numer. Heat Transfer, Part B 42 (2002) 215-230
9. Liu C.-S. Group preserving scheme for backward heat conduction problems. Int. J. Heat Mass Transfer 47 (2004) 2567-2576
10. xtx on a strip. Arch. Rational Mech. Anal. 19 (1965) 100-116
11. Yildiz B., and Özdemir M. Stability of the solution of backward heat equation on a weak compactum. Appl. Math. Comput. 111 (2000) 1-6
12. Yildiz B., Yetiş H., and Sever A. A stability estimate on the regularized solution of the backward heat equation. Appl. Math. Comput. 135 (2003) 561-567
13. Eldén L. Approximations for a Cauchy problem for the heat equation. Inverse Probl. 3 (1987) 263-273
14. Chen P.J., and Gurtin M.E. On a theory of heat conduction involving two temperatures. ZAMP 19 (1968) 614-627
15. Barenblatt G.I., Zheltov Iu.P., and Kochina I.N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata). Priklad. Mat. Mekh. 24 (1960) 852-864
16. Coleman B.D., and Noll W. An approximation theorem for functionals, with application in continuum mechanics. Arch. Rational Mech. Anal. 6 (1960) 355-370