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

Author

Listed:
  • Hossein Jafari

    (University of Mazandaran
    University of South Africa, UNISA)

  • Afshin Babaei

    (University of Mazandaran)

  • Seddigheh Banihashemi

    (University of Mazandaran)

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.

Suggested Citation

  • Hossein Jafari & Afshin Babaei & Seddigheh Banihashemi, 2019. "A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 688-704, November.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:2:d:10.1007_s10957-019-01576-x
    DOI: 10.1007/s10957-019-01576-x
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    References listed on IDEAS

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    1. Zui-Cha Deng & Y.-C. Hon & Liu Yang, 2014. "An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 890-910, March.
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