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Determination of the Time-Dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity

  • M. S. HusseinEmail author
  • D. Lesnic
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)

Abstract

In this paper, we consider an inverse problem of determining the time-dependent thermal conductivity from Cauchy data in a one-dimensional heat equation with space-dependent heat capacity. The parabolic partial differential equation is discretised using the finite -difference method and the inverse problem is recast as a nonlinear least-squares minimization. This is solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed showing that accurate and stable numerical solutions are achieved.

Keywords

Inverse problem Finite-difference method Thermal conductivity 

Notes

Acknowledgments

M.S. Hussein would like to thank the Higher Committee of Education Development in Iraq (HCEDiraq) for their financial support.

References

  1. 1.
    Cannon, J.R., DuChateau, P.: Determining unknown coefficients in a nonlinear heat conduction problem. SIAM J. Appl. Math. 24, 298–314 (1973)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Doris, H.G., Peralta, J., Luis, E.O.: Regularization algorithm within two parameters for the identification of the heat conduction coefficient in the parabolic equation. Math. Comput. Model. 57, 1990–1998 (2013)zbMATHCrossRefGoogle Scholar
  3. 3.
    Ivanchov, M.I.: Inverse Problems for Equations of Parabolic Type. VNTL Publications, Lviv, Ukraine (2003)Google Scholar
  4. 4.
    Lesnic, D., Yousefi, S.A., Ivanchov, M.: Determination of a time-dependent diffusivity from nonlocal conditions. J. Appl. Math. Comput. 41, 301–320 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford Applied Mathematics and Computing Science Series, Third Edition (1985)Google Scholar
  6. 6.
    Mathworks R2012 Documentation Optimization Toolbox-Least Squares (Model Fitting) Algorithms. www.mathworks.com/help/toolbox/optim/ug/brnoybu.html
  7. 7.
    Wang, Y., Yang, C., Yagola, A.: Optimization and Regularization for Computational Inverse Problems and Applications. Springer-Verlag, Berlin (2011)CrossRefGoogle Scholar
  8. 8.
    Wang, P., Zheng, K.: Determination of an unknown coefficient in a nonlinear heat equation. J. Math. Anal. Appl. 271, 525–533 (2002)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of LeedsLeedsUK
  2. 2.Department of MathematicsUniversity of Baghdad, College of ScienceBaghdadIraq

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