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Reconstruction of Timewise Term for the Nonlocal Diffusion Equation from an Additional Condition

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Abstract

The inverse problem of reconstructing the timewise term along with the temperature in the nonlocal diffusion equation with initial and boundary conditions and additional measurement (an integral and partial heat flux) is, for the first time, numerically investigated. This inverse problem appears extensively in the modeling of various phenomena in engineering and physics. The inverse problem considered in this paper has a unique solution. A Crank–Nicolson FDM is applied as a direct solver. The resulting nonlinear problem is solved using the MATLAB subroutine to minimize the objective functional. The Tikhonov regularization method is applied where necessary. A pair of examples, with smooth and non-smooth continuous timewise term, are discussed to assess the accuracy and stability of the numerical solutions.

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Acknowledgements

The comments and suggestions made by the referees are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia

    M. J. Huntul & Mohammad Tamsir

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  1. M. J. Huntul
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  2. Mohammad Tamsir
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Correspondence to M. J. Huntul.

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Huntul, M.J., Tamsir, M. Reconstruction of Timewise Term for the Nonlocal Diffusion Equation from an Additional Condition. Iran J Sci Technol Trans Sci 44, 1827–1838 (2020). https://doi.org/10.1007/s40995-020-00980-7

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  • DOI: https://doi.org/10.1007/s40995-020-00980-7

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