Sequential solution of the sideways heat equation by windowing of the data

Inverse Problems in Engineering

Volumn 11, Issue 2, 2003, Pages 91-103

  Berntsson, Fredrik ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Ill posed; Sequential method; Sideways heat equation

Indexed keywords

DATA ACQUISITION; HEAT CONDUCTION; MATHEMATICAL MODELS; THERMAL VARIABLES MEASUREMENT;

HEAT EQUATION;

PROBLEM SOLVING;

EID: 0037657974     PISSN: 10682767     EISSN: None     Source Type: Journal    
DOI: 10.1080/1068276021000048564     Document Type: Article

References (18)

1. J.V. Beck and B. Blackwell (1988). Inverse problems. In: W.J. Minkowycz, E.M. Sparrow, G.E. Scheider and R.H. Pletcher (Eds.), Handbook of Numerical Heat Transfer, Chapter 19, pp. 787-834. J. Wiley and Sons, New York.
2. F. Berntsson (1999). A spectral method for solving the sideways heat equation. Inverse Problems, 15, 891-906.
3. F. Berntsson, L. Eidén, R. Garcia-Padron and D. Loyd (1997). A comparison of three numerical methods for an inverse heat conduction problem and an industrial application. In: R.W. Lewis (Ed.), Proceedings of the 10th International Conference on Numerical Methods in Thermal Problems Swansea.
4. A.S. Carasso (1982). Determining surface temperatures from interior observations. SIAM J. Appl. Math., 42, 558-574.
5. L. Eidén (1997). Solving the sideways heat equation by a 'method of lines'. J. Heat Transfer, Trans. ASME, 119, 406-412.
6. L. Eidén., F. Berntsson and T. Regińska (2000). Wavelet and fourier methods for solving the sideways heat equation. SIAM J. Sci. Comput., 21(6), 2187-2205.
7. H. Engl, M. Hanke and A. Neubauer (1996). Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht, the Netherlands.
8. B. Gustafsson, H.-O. Kreiss and J. Öliger (1995). Time Dependent Problems and Difference Methods. Wiley Interscience, New York.
9. Dinh Nho Hào, H.-J. Reinhardt and A. Schneider (2001). Numerical solution to a sideways parabolic equation. Internat. J. Numer. Methods Engrg., 50(5), 1253-1267.
10. J.P. Holman (1992). Heat Transfer, 7th Edn. MCGraw Hill, New York.
11. P. Lamm (1995). Future-sequential regularization methods for ill-posed Volterra equations. Applications to the inverse heat conduction problem. J. Math. Anal. Appl., 195(2), 469-494.
12. H.A. Levine (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), CXXXIV, 267-286.
13. C.E. Mejia and D.A. Murio (1996). Numerical solution of generalized IHCP by discrete mollification. Computers Math. Appl, 32, 33-50.
14. D.A. Murio (1993). The Mollification Method and the Numerical Solution of Ill-Posed Problems. J. Wiley & Sons, New York.
15. T. Reginska and L. Eiden (1997). Solving the sideways heat equation by a wavelet-Galerkin method. Inverse Problems, 13, 1093-1106.
16. G.D. Smith (1985). Numerical Solution of Partial Differential Equations, 3rd Edn. Oxford University Press, Oxford.
17. U. Tautenhahn (1997). Optimal stable approximations for the sideways heat equation. J. Inv. Ill-Posed Problems, 5, 287-307.
18. S. Zhan and D.A. Murio (1998). Identification of parameters in one-dimensional IHCP. Comput. Math. Appl., 35(3), 1-16.