A quasi-boundary semi-analytical approach for two-dimensional backward heat conduction problems

Computers, Materials and Continua

Volumn 15, Issue 1, 2010, Pages 45-66

  Chang, Chih Wen ^a   Liu, Chein Shan ^b   Chang, Jiang Ren ^c  

^a NATIONAL CENTER FOR HIGH PERFORMANCE COMPUTING   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

Backward heat conduction problem; Fourier series; Fredholm integral equation; Ill posed problem; Regularized solution

Indexed keywords

BACKWARD HEAT CONDUCTION PROBLEM; CLOSED FORM; FOURIER-SERIES EXPANSION; FREDHOLM INTEGRAL EQUATIONS; HEAT CONDUCTION PROBLEMS; ILL POSED PROBLEM; KERNEL FUNCTION; NUMERICAL EXAMPLE; REGULARIZATION PARAMETERS; SEMI-ANALYTICAL; SEMI-ANALYTICAL METHODS; TEMPERATURE FIELD;

FOURIER ANALYSIS; HARMONIC ANALYSIS; HEAT CONDUCTION; INTEGRAL EQUATIONS; PROBLEM SOLVING; TWO DIMENSIONAL;

FOURIER SERIES;

EID: 77952843312     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Ames, K. A.; Cobb, S. S. (1997): Continuous dependence on modeling for related Cauchy problems of a class of evolution equations. J. Math. Anal. Appl., vol.215, pp. 15-31.
2. Ames, K. A.; Clark, G. W.; Epperson, J. F.; Oppenheimer, S. F. (1998): A comparison of regularizations for an ill-posed problem. Math. Comput., vol.67, pp. 1451-1471.
3. Boussetila, N.; Rebbani, F. (2006): Optimal regularization method for ill-posed Cauchy problems. Electronic J. Diff. Equations, vol.2006, pp. 1-15.
4. Chang, C.-W.; Liu, C.-S.; Chang, J.-R. (2005): A group preserving scheme for inverse heat conduction problems. CMES: Computer Modeling in Engineering & Sciences, vol.10, pp. 13-38.
5. Chang, C.-W.; Liu, C.-S.; Chang, J.-R. (2008): A new shooting method for quasi-boundary regularization of multi-dimensional backward heat conduction problems. J. Chinese Insti. Eng., vol.32, pp. 307-318.
6. Chang, J.-R.; Liu, C.-S.; Chang, C.-W. (2007): A new shooting method for quasi-boundary regularization of backward heat conduction problems. Int. J. Heat Mass Transfer, vol.50, pp. 2325-2332.
7. Denche, M.; Bessila, K. (2005): A modified quasi-boundary value method for ill-posed problems. J. Math. Anal. Appl., vol.301, pp. 419-426.
8. Huang, Y.; Zheng, Q. (2005): Regularization for a class of ill-posed Cauchy problems. Proc. A. M. S., vol.133, pp. 3005-3012.
9. Iijima, K. (2004): Numerical solution of backward heat conduction problems by a high order lattice-free finite difference method. J. Chinese Inst. Engineers, vol.27, pp. 611-620.
10. Lattés, R.; Lions, J. L. (1969): The Method of Quasireversibility, Applications to Partial Differential Equations. Elsevier, New York.
11. Liu, C.-S. (2001): Cone of non-linear dynamical system and group preserving schemes. Int. J. Non-Linear Mech., vol.36, pp. 1047-1068.
12. Liu, C.-S. (2004): Group preserving scheme for backward heat conduction problems. Int. J. Heat Mass Transfer, vol.47, pp. 2567-2576.
13. Liu, C.-S. (2007a): Elastic torsion bar with arbitrary cross-section using the Fredholm integral equations. CMC: Computers, Materials & Continua, vol.5, pp. 31-42.
14. Liu, C.-S. (2007b): A meshless regularized integral equation method for Laplace equation in arbitrary interior or exterior plane domains. CMES: Computer Modeling in Engineering & Sciences, vol.19, pp. 99-109.
15. Liu, C.-S. (2007c): A MRIEM for solving the Laplace equation in the doublyconnected domain. CMES: Computer Modeling in Engineering & Sciences, vol.19, pp. 145-161.
16. Liu, C.-S. (2009a): Solving the inverse problems of Laplace equation to determine the Robin coefficient/cracks' position inside a disk. CMES: Computer Modeling in Engineering & Sciences, vol.40, pp. 1-28.
17. Liu, C.-S. (2009b): A new method for Fredholm integral equations of 1D backward heat conduction problems. CMES: Computer Modeling in Engineering & Sciences, vol.47, pp. 1-21.
18. Liu, C.-S.; Chang, C.-W.; Chang, J.-R. (2006): Past cone dynamics and backward group preserving schemes for backward heat conduction problems. CMES: Computer Modeling in Engineering & Sciences, vol.12, pp. 67-81.
19. Liu, C.-S.; Chang, C.-W.; Chang, J.-R. (2009): The backward group preserving scheme for 1D backward in time advection-dispersion equation. CMC: Computer, Materials & Continua, vol.9, pp. 111-135.
20. Liu, C.-S.; Chang, C. W.; Chiang, C. Y. (2008): A regularized integral equation method for the inverse geometry heat conduction problem. Int. J. Heat Mass Transfer, vol.51, pp. 5380-5388.
21. Liu, J. (2002): Numerical Solution of Forward and Backward Problem for 2-D Heat Conduction Equation. J. Comput. Appl. Math., vol.145, pp. 459-482.
22. Mel'nikova, I. V. (1992): Regularization of ill-posed differential problems. Siberian Math. J., vol.33, pp. 289-298.
23. Mera, N. S. (2005): The method of fundamental solutions for the backward heat conduction problem. Inv. Prob. Sci. Eng., vol.13, pp. 65-78.
24. Miller, K. (1973): Stabilized quasireversibility and other nearly best possible methods for non-well posed problems. Lecture Notes in Math. Springer-Verlag, Berlin, vol.316, pp. 161-176.
25. Showalter, R. E. (1983): Cauchy problem for hyper-parabolic partial differential equations. In Trends in the Theory and Practice of Non-Linear Analysis, Elsevier, Amsterdam, pp. 421-425.
26. Showalter, R. E.; Ting, T. W. (1970): Pseudo-parabolic partial differential equations. SIAM J. Math. Anal., vol.1, pp. 1-26.
27. Tricomi, F. G. (1985): Integral Equations. Dover Publications, New York.