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)


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.


Inverse problem Finite-difference method Thermal conductivity 



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


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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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