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

Hossein Jafari (), Afshin Babaei () and Seddigheh Banihashemi
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Hossein Jafari: University of Mazandaran
Afshin Babaei: University of Mazandaran
Seddigheh Banihashemi: University of Mazandaran

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 2, No 14, 688-704

Abstract: 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.

Keywords: Inverse problem; Reaction–diffusion–convection equation; Sixth-kind Chebyshev polynomials; Collocation method; Mollification; Error estimate; 35R30; 35K15; 41A50; 65M70 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01576-x

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