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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
Reconstructing unknown nonlinear boundary conditions in a time-fractional inverse reaction–diffusion–convection problem
Type
JournalPaper
Keywords
Caputo’s fractional derivative, inverse problem, marching scheme, mollification, time-fractional reaction–diffusion– convection equation
Year
2018
Journal NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
DOI
Researchers Afshin Babaei ، ُSeddighe Banihashemi

Abstract

This paper has focused on unknown functions identification in nonlinear boundary conditions of an inverse problem of a time-fractional reaction–diffusion–convection equation. This inverse problem is generally ill-posed in the sense of stability, that is, the solution of problem does not depend continuously on the input data. Thus, a combination of the mollification regularization method with Gauss kernel and a finite difference marching scheme will be introduced to solve this problem. The generalized cross-validation choice rule is applied to find a suitable regularization parameter. The stability and convergence of the numerical method are investigated. Finally, two numerical examples are provided to test the effectiveness and validity of the proposed approach.