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dc.contributor.authorZeidabadi, Hameden_US
dc.contributor.authorPourgholi, Rezaen_US
dc.contributor.authorHosseini, Abbasen_US
dc.date.accessioned2022-07-08T10:06:05Z
dc.date.available2022-07-08T10:06:05Z
dc.date.issued2022
dc.identifier.citationZeidabadi, H., Pourgholi, R. & Hosseini, A. (2022). Determination of a nonlinear source term in a reaction-diffusion equation by using finite element method and radial basis functions method. TWMS Journal of Applied and Engineering Mathematics, 12(3), 768-785.en_US
dc.identifier.issn2146-1147
dc.identifier.issn2587-1013
dc.identifier.urihttps://hdl.handle.net/11729/4664
dc.identifier.urihttp://jaem.isikun.edu.tr/web/index.php/archive/116-vol12no3/863
dc.description.abstractIn this paper, two numerical methods are presented to solve a nonlinear inverse parabolic problem of determining the unknown reaction term in the scalar reactiondiffusion equation. In the first method, the finite element method will be used to discretize the variational form of the problem and in the second method, we use the radial basis functions (RBFs) method for spatial discretization and finite-difference for time discretization. Usually, the matrices obtained from the discretization of the equations are ill-conditioned, especially in higher-dimensional problems. To overcome such difficulties, we use Tikhonov regularization method. In fact, this work considers a comparative study between the finite element method and radial basis functions method. As we will see, these methods are very useful and convenient tools for approximation problems and they are stable with respect to small perturbation in the input data. The effectiveness of the proposed methods are illustrated by numerical examples.en_US
dc.language.isoengen_US
dc.publisherIşık University Pressen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectNonlinear inverse problemen_US
dc.subjectParabolic equationsen_US
dc.subjectFinite element methoden_US
dc.subjectRadial basis functions methoden_US
dc.subjectLeast square methoden_US
dc.subjectTikhonov regularization methoden_US
dc.subjectStability analysisen_US
dc.titleDetermination of a nonlinear source term in a reaction-diffusion equation by using finite element method and radial basis functions methoden_US
dc.typearticleen_US
dc.description.versionPublisher's Versionen_US
dc.relation.journalTWMS Journal of Applied and Engineering Mathematicsen_US
dc.identifier.volume12
dc.identifier.issue3
dc.identifier.startpage768
dc.identifier.endpage785
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıen_US


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