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A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem

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Abstract

In this paper, we consider an inverse reaction–diffusion–convection problem in which one of the boundary conditions is unknown. A sixth-kind Chebyshev collocation method will be proposed to solve numerically this problem and to obtain the unknown boundary function. Since this inverse problem is generally ill-posed, to find an optimal stable solution, we will utilize a regularization method based on the mollification technique with the generalized cross-validation criterion. The error estimate of the numerical solution is investigated. Finally, to authenticate the validity and effectiveness of the proposed algorithm, some numerical test problems are presented.

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Authors and Affiliations

  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    Hossein Jafari, Afshin Babaei & Seddigheh Banihashemi

  2. Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria, 0003, South Africa

    Hossein Jafari

Authors
  1. Hossein Jafari
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  2. Afshin Babaei
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  3. Seddigheh Banihashemi
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Correspondence to Hossein Jafari.

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Jafari, H., Babaei, A. & Banihashemi, S. A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem. J Optim Theory Appl 183, 688–704 (2019). https://doi.org/10.1007/s10957-019-01576-x

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  • DOI: https://doi.org/10.1007/s10957-019-01576-x

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