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Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
A Novel Approach for Solving an Inverse Reaction–Diffusion–Convection Problem
Type
JournalPaper
Keywords
Inverse problem, Reaction–diffusion–convection equation, Sixth-kind Chebyshev polynomials, Collocation method, Mollification, Error estimate
Year
2019
Journal JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
DOI
Researchers Hossein Jafari ، Afshin Babaei ، ُSeddighe Banihashemi

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.