Solving an inverse heat conduction problem by a “method of lines”

Journal of Heat Transfer

Volumn 119, Issue 3, 1997, Pages 406-412

  Elden L ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Numerical methods

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; INVERSE PROBLEMS; PROBLEM SOLVING;

CAUCHY PROBLEMS; INVERSE HEAT CONDUCTION PROBLEM; METHOD OF LINES;

HEAT CONDUCTION;

EID: 0031209056     PISSN: 00221481     EISSN: 15288943     Source Type: Journal    
DOI: 10.1115/1.2824112     Document Type: Article

References (28)

1. Beck, J. V., and Blackwell, B., 1988, “Inverse problems,” Handbook of Numerical Heat Transfer, W. J. Minkowycz et al., eds., chap. 19, pp. 787-834, John Wiley & Sons, New York
2. Beck, J. V., Blackwell, B., and Clair, S. R., 1985, Inverse Heat Conduction, IU-Posed Problems, Wiley, New York
3. Cannon, J. R., 1984, The One-Dimensional Heat Equation, Addison-Wesley, Reading, MA
4. Carasso, A. S., 1982, “Determining Surface Temperatures From Interior Observations,” SIAM J. Appl. Math., Vol. 42, pp. 558-574
5. Carasso, A. S., 1992, “Space Marching Difference Schemes in the Nonlinear Inverse Heat Conduction Problem,” Inverse Problems, Vol. 8, pp. 25-43
6. Carasso, A. S., 1993, “Slowly Divergent Space Marching Schemes in the Inverse Heat Conduction Problem,” Numerical Heat Transfer, part B, Vol. 23, pp. 111-126
7. Carasso, A. S., 1994, “Overcoming Holder Continuity in Ill-Posed Continuation Problems,” SIAM J. Numer. Anal, Vol, 31, pp. 1535-1557
8. Dahlquist G., and Björck, A., 1974, Numerical Methods, Prentice-Hall, Englew-odd Cliffs, N.J
9. Eiden, L., 1988, “Hyperbolic Approximations for a Cauchy Problem for the Heat Equation,” Inverse Problems, Vol. 4, pp. 59-70
10. Eiden, L., 1995, “Numerical Solution of the Sideways Heat Equation,” Inverse Problems in Diffusion Processes, H. Engl and W. Rundell, eds., SIAM, PA, pp. 130-150
11. Eiden, L., 1995, “Numerical Solution of the Sideways Heat Equation by Difference Approximation in Time,” Inverse Problems, Vol. 11, pp. 913-923
12. Engl, H. W., andManselli, P., 1989, “Stability Estimates and Regularization for an Inverse Heat Conduction Problem in Semi-Infinite and Finite Time Intervals,” Numer. Funct. Anal. Optimiz., Vol. 10, pp. 517-540
13. Gear, C. W., 1971, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J
14. Golub, G. H., and Van Loan, C. F., 1989, Matrix Computations, 2nd ed., Johns Hopkins Press, Baltimore, MD
15. Guo, L., and Murio, D., 1991, “A Mollified Space-Marching Finite-Difference Algorithm for the Two-Dimensional Inverse Heat Conduction Problem With Slab Symmetry,” Inverse Problems, Vol. 7, pp. 247-259
16. Guo, L., Murio, D. A., and Roth, C., 1990, “A Mollified Space Marching Finite Differences Algorithm for the Inverse Heat Conduction Problem With Slab Symmetry,” Computers Math. Applic., Vol. 19, pp. 75-89
17. Hairer, E., Nprsett, S. P., and Wanner, G., 1993, Solving Ordinary Differential Equations I, 2nd ed., Springer, Berlin
18. Hairer, E., and Wanner, G., 1991, Solving Ordinary Differential Equations II, Springer, Berlin
19. Knabner, P.F and Vessella, S.1987, “Stability Estimates for Ill-Posed Cauchy Problems for Parabolic Equations,” Inverse and Ill-Posed Problems, Academic Press H. W. Engl and C. W. Groetsch, eds., St. Wolfgang, Austria, pp. 351-368
20. Levine, H. A., 1983, “Continuous Data Dependence, Regularization, and a Three Lines Theorem for the Heat Equation With Data in a Space Like Direction,” Ann. Mat. Pura Appl. (IV), Vol. CXXXIV, pp. 267-286
21. Matlab, 1992, Reference Guide, Mathworks Inc., Natick Mass
22. Murio, D. A., 1989, “The Mollification Method and the Numerical Solution of the Inverse Heat Conduction Problem by Finite Differences,” Computers Math. Applic., Vol. 10, pp. 1385-1396
23. Murio, D. A., 1993, The Mollification Method and the Numerical Solution of Ill-Posed Problems, John Wiley & Sons, New York
24. Murio, D. A., and Guo, L., 1990, “A Stable Space Marching Finite Differences Algorithm for the Inverse Heat Conduction Problem With no Initial Filtering Procedure,” Computers Math. Applic., Vol. 19, No. 10, pp. 35-50
25. Reginska, T., and Elden, L., 1996, “Numerical Solution of the Sideways Heat Equation by Meyer Wavelets,” Technical Report Report LiTH-MAT-R-96, Department of Mathematics, Linköping University, in press
26. Seidman, T., and Eiden, L., 1990, “An Optimal Filtering Method for the Sideways Heat Equation,” Inverse Probl, Vol. 6, pp. 681-696
27. Smith, G. D., 1978, Numerical Solution of Partial Differential Equations, 2nd ed., Oxford University Press, Oxford
28. Weber, C. F., 1981, “Analysis and Solution of the Ill-Posed Inverse Heat Conduction Problem,” Int. J. Heat Mass Transfer, Vol. 24, pp. 1783-1792