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Inverse Problems in Science and Engineering Volume 15, 2007 - Issue 3
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Original Articles

Numerical analysis of an ill-posed Cauchy problem for a convection--diffusion equation

Z. RanjbarDepartment of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
&
L. EldénDepartment of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Pages 191-211 | Received 21 Sep 2005, Accepted 14 Dec 2005, Published online: 25 Apr 2007

References

  • Beck, JV, Blackwell, B, and Clair, SR, 1985. Inverse Heat Conduction. Ill-Posed Problems. Wiley: New York; 1985.
  • Berntsson, F, 1999. A spectral method for solving the sideways heat equation, Inverse Problems 15 (1999), pp. 891–906.
  • Berntsson, F, 2001. Numerical methods for solving a non-characteristic Cauchy problem for a parabolic equation. Department of Mathematics, Linköping University; 2001, Technical Report LiTH-MAT-R-2001-17.
  • Brown, JW, and Churchill, RV, 1996. Complex Variables and Applications. New York: McGraw-Hill, Inc; 1996.
  • Carasso, AS, 1982. Determining surface temperatures from interior observations, SIAM Journal of Applied Mathematics 42 (1982), pp. 558–574.
  • Eldén, L, 1983. "The numerical solution of a non-characteristic Cauchy problem for a parabolic equation". In: Deuflhard, P, and Hairer, E, eds. Numerical Treatment of Inverse Problems in Differential and Integral Equations, Proceedings of an International Workshop, 1982. Heidelberg, Boston: Birkhäuser; 1983. pp. 246–268.
  • Eldén, L, 1995. "Numerical solution of the sideways heat equation". In: Engl, H, and Rundell, W, eds. Inverse Problems in Diffusion Processes. Philadelphia: SIAM; 1995. pp. 130–150.
  • Eldén, L, 1995. Numerical solution of the sideways heat equation by difference approximation in time, Inverse Problems 11 (1995), pp. 913–923.
  • Eldén, L, 1997. Solving the sideways heat equation by a ‘method of lines', Journal of Heat Transfer, Transactions of the ASME 119 (1997), pp. 406–412.
  • Eldén, L, Berntsson, F, and Regińska, T, 2000. Wavelet and Fourier methods for solving the sideways heat equation., SIAM Journal of Scientific Computing 21 (6) (2000), pp. 2187–2205.
  • Engl, H, Hanke, M, and Neubauer, A, 1996. Regularization of Inverse Problems. Kluwer Academic Publishers: Dordrecht, The Netherlands; 1996.
  • Hairer, E, and Wanner, G, 1991. Solving Ordinary Differential Equations II. Springer: Berlin; 1991.
  • Dinh Nho Hào, , 1998. Methods for Inverse Heat Conduction Problems. Frankfurt am Main: Peter Lang; 1998.
  • Hundsdorfer, W, and Verwer, JG, 2003. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer: Berlin, New York; 2003.
  • Knabner, P, and Vessella, S, 1988. The optimal stability estimate for some ill-posed Cauchy problems for a parabolic equation, Mathematical Methods in the Applied Sciences 10 (1988), pp. 575–583.
  • Lamm, P, and Eldén, L, 1997. Numerical solution of first-kind Volterra equations by sequential Tikhonov regularization., SIAM Journal of Numerical Analysis 34 (1997), pp. 1432–1450.
  • Linz, P, 1980. "A survey of methods for the solution of Volterra integral equations of the first kind". In: Anderssen, RS, de Hoog, FR, and Lukas, MA, eds. The Application and Numerical Solution of Integral Equations. The Hague: Sijthoff & Noordhoff, Alphen aan den Rijn; 1980. pp. 183–194.
  • Manselli, P, and Miller, K, 1980. Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite side, Annali di Matematica Pura ed Applicata 123 (1980), pp. 161–183.
  • Smith, W.R and Wake, G.C., 1990. Mathematical analysis: an inverse problem arising in convective-diffusive flow, IMA Journal of Applied Mathematics 45 (1990), pp. 225–231.
  • Strang, G, 1986. Introduction to Applied Mathematics. Cambridge Press: Wellesley, USA; 1986.

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