Please use this identifier to cite or link to this item: https://hdl.handle.net/11499/30287
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dc.contributor.authorErdogan, U.-
dc.contributor.authorSari, M.-
dc.contributor.authorKoçak, Hüseyin-
dc.date.accessioned2020-06-08T12:12:16Z
dc.date.available2020-06-08T12:12:16Z
dc.date.issued2019-
dc.identifier.issn0961-5539-
dc.identifier.urihttps://hdl.handle.net/11499/30287-
dc.identifier.urihttps://doi.org/10.1108/HFF-05-2017-0198-
dc.description.abstractPurpose: The purpose of this study is to propose a non-classical method to obtain efficient and accurate numerical solutions of the advection–diffusion–reaction equations. Design/methodology/approach: Unlike conventional numerical methods, this study proposes a numerical scheme using outer Newton iteration applied to a time-dependent PDE. The linearized time dependent PDE is discretized by trapezoidal rule, which is second order in time, and by spline-based finite difference method of fourth order in space. Findings: Using the proposed technique, even when relatively large time step sizes are used in computations, the efficiency of the proposed procedure is very clear for the numerical examples in comparison with the existing classical methods. Originality/value: This study, unlike these classical methods, proposes an alternative approach based on linearizing the nonlinear problem at first, and then discretizing it by an appropriate scheme. This technique helps to avoid considering the convergence issues of Newton iteration applied to nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. The linearized PDE can be solved by implicit time integrator, which enables the use of large time step size. © 2018, Emerald Publishing Limited.en_US
dc.language.isoenen_US
dc.publisherEmerald Group Publishing Ltd.en_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAdvection-diffusion-reaction equationsen_US
dc.subjectFréchet derivativeen_US
dc.subjectHybrid spline difference methoden_US
dc.subjectLinearizationen_US
dc.subjectSpace discretizationen_US
dc.subjectTime discretizationen_US
dc.subjectAdvectionen_US
dc.subjectAlgebraen_US
dc.subjectControl nonlinearitiesen_US
dc.subjectDiffusionen_US
dc.subjectFinite difference methoden_US
dc.subjectIterative methodsen_US
dc.subjectNon Newtonian flowen_US
dc.subjectDesign/methodology/approachen_US
dc.subjectHybrid spline difference methodsen_US
dc.subjectNon-linear algebraic systemen_US
dc.subjectNumerical treatmentsen_US
dc.subjectReaction equationsen_US
dc.subjectSpace discretizationsen_US
dc.subjectNumerical methodsen_US
dc.titleEfficient numerical treatment of nonlinearities in the advection–diffusion–reaction equationsen_US
dc.typeArticleen_US
dc.identifier.volume29en_US
dc.identifier.issue1en_US
dc.identifier.startpage132
dc.identifier.startpage132en_US
dc.identifier.endpage145en_US
dc.authorid0000-0001-9683-6096-
dc.identifier.doi10.1108/HFF-05-2017-0198-
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.scopus2-s2.0-85056196460en_US
dc.identifier.wosWOS:000457050100006en_US
dc.identifier.scopusqualityQ2-
dc.ownerPamukkale University-
item.grantfulltextnone-
item.languageiso639-1en-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.dept08.04. Business Administration-
Appears in Collections:İktisadi ve İdari Bilimler Fakültesi Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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