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

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Finite Difference Methods,Theory and Applications (FDM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9045))

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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.

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References

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Leeds, Ls2 9jt, Leeds, UK

    M. S. Hussein & D. Lesnic

  2. Department of Mathematics, University of Baghdad, College of Science, Baghdad, Iraq

    M. S. Hussein

Authors
  1. M. S. Hussein
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  2. D. Lesnic
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Corresponding author

Correspondence to M. S. Hussein .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Hussein, M.S., Lesnic, D. (2015). Determination of the Time-Dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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