Abstract
In this paper, a non-linear source term is approximated for an inverse parabolic problem using final observations as additional data. The inverse problem is solved as an optimization problem where objective function is minimized by an iterative algorithm namely the Levenberg–Marquardt Method. Sensitivity analysis is used to find how many terms of the polynomial basis functions are suitable for the source term approximation. Results show that for different boundary conditions, different numbers of the basis functions are appropriate, without considering functional forms of the source term. To examine the accuracy of approximations, some test examples are carried out. The algorithm seems to be very sharp if the corresponding direct problem has a smaller solution’s maximum.
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Communicated by Cristina Turner.
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Shidfar, A., Jazbi, B. & Alinejadmofrad, M. Numerical approximation of a non-linear source term for an inverse parabolic problem. Comp. Appl. Math. 34, 363–373 (2015). https://doi.org/10.1007/s40314-014-0121-3
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DOI: https://doi.org/10.1007/s40314-014-0121-3