Numerical solution of singularlyperturbed convection-diffusion equations

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dc.citation.conference7th International youth science forum «Litteris et Artibus»
dc.citation.epage427
dc.citation.journalTitleLitteris et Artibus : матеріали
dc.citation.spage425
dc.contributor.affiliationYuzuncu Yil University, Faculty of Sciences, Department of Mathematics, Van, Turkey
dc.contributor.authorSakar, Mehmet Giyas
dc.contributor.authorErdogan, Fevzi
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.coverage.temporal23–25 листопада 2017 року
dc.coverage.temporal23–25 November, 2017
dc.date.accessioned2018-04-12T13:05:58Z
dc.date.available2018-04-12T13:05:58Z
dc.date.created2017-12-23
dc.date.issued2017-12-23
dc.description.abstractIn this paper, a new method is given for solving singularly perturbed convection-diffusion problems. The present method is based on combining the asymptotic expansion method and the variational iteration method (VIM) with an auxiliary parameter. Numerical results show that the present method can provide very accurate numerical solutions not only in the boundary layer, but also away from the layer.
dc.format.extent425-427
dc.format.pages3
dc.identifier.citationSakar M. G. Numerical solution of singularlyperturbed convection-diffusion equations / Mehmet Giyas Sakar, Fevzi Erdogan // Litteris et Artibus : proceedings, 23–25 November, 2017. — Lviv : Lviv Polytechnic Publishing House, 2017. — P. 425–427. — (9th International academic conference «Computer science & engineering 2017» (CSE-2017)).
dc.identifier.citationenSakar M. G. Numerical solution of singularlyperturbed convection-diffusion equations / Mehmet Giyas Sakar, Fevzi Erdogan // Litteris et Artibus : proceedings, 23–25 November, 2017. — Lviv : Lviv Polytechnic Publishing House, 2017. — P. 425–427. — (9th International academic conference «Computer science & engineering 2017» (CSE-2017)).
dc.identifier.isbn978-966-941-108-2
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/40451
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Polytechnic Publishing House
dc.relation.ispartofLitteris et Artibus : матеріали, 2017
dc.relation.ispartofLitteris et Artibus : proceedings, 2017
dc.relation.references[1] F. Geng, M. Cui, Analytical approximation to solutions of singularly perturbed boundary value prob- lems, Bull. Malays. Math. Sci. Soc. 33 (2) (2010) 221-232.
dc.relation.references[2] Y. N. Reddy, P. P. Chakravarthy, Numerical patching method for singularly perturbed two-point boundary value problems using cubic splines, Applied Mathematics and Computation 149 (2004) 441-468.
dc.relation.references[3] M. K. Kadalbajoo, A. S. Yadaw, D. Kumar, Comparative study of singularly perturbed twopoint BVPs via: Fitted-mesh finite difference method, B-spline collocation method and finite element method, Applied Mathematics and Computation 204 (2) (2008) 713-725.
dc.relation.references[4] P. Zhu, S. Xie, Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type, Applied NumericalMathematics 76 (2014) 48-59.
dc.relation.references[5] M. Brdar, H. Zarin, A singularly perturbed problem with two parameters on a Bakhvalov-type mesh, Journal of Computational and Applied Mathematics 292 (2016) 307-319.
dc.relation.references[6] E. P. Doolan, J. J. H. Miller, W. H. A. Schilders, Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980.
dc.relation.references[7] J. H. He, Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2 (4) (1997) 235-236.
dc.relation.references[8] M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, in:S.Nemat-Nasser(Ed.), Variational Method in the Mechanics of Solids, Pergamon Press, New York, 1978, pp. 156-162.
dc.relation.references[9] M. G. Sakar, O. Saldır, Improving variational iteration method with auxiliary parameter for nonlinear time-fractional partial differential equations, Journal of Optimization Theory and Applications 174 (2) (2017) 530-549.
dc.relation.references[10] Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat. 15 2003-2016 (2010).
dc.relation.referencesen[1] F. Geng, M. Cui, Analytical approximation to solutions of singularly perturbed boundary value prob- lems, Bull. Malays. Math. Sci. Soc. 33 (2) (2010) 221-232.
dc.relation.referencesen[2] Y. N. Reddy, P. P. Chakravarthy, Numerical patching method for singularly perturbed two-point boundary value problems using cubic splines, Applied Mathematics and Computation 149 (2004) 441-468.
dc.relation.referencesen[3] M. K. Kadalbajoo, A. S. Yadaw, D. Kumar, Comparative study of singularly perturbed twopoint BVPs via: Fitted-mesh finite difference method, B-spline collocation method and finite element method, Applied Mathematics and Computation 204 (2) (2008) 713-725.
dc.relation.referencesen[4] P. Zhu, S. Xie, Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type, Applied NumericalMathematics 76 (2014) 48-59.
dc.relation.referencesen[5] M. Brdar, H. Zarin, A singularly perturbed problem with two parameters on a Bakhvalov-type mesh, Journal of Computational and Applied Mathematics 292 (2016) 307-319.
dc.relation.referencesen[6] E. P. Doolan, J. J. H. Miller, W. H. A. Schilders, Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980.
dc.relation.referencesen[7] J. H. He, Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2 (4) (1997) 235-236.
dc.relation.referencesen[8] M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, in:S.Nemat-Nasser(Ed.), Variational Method in the Mechanics of Solids, Pergamon Press, New York, 1978, pp. 156-162.
dc.relation.referencesen[9] M. G. Sakar, O. Saldır, Improving variational iteration method with auxiliary parameter for nonlinear time-fractional partial differential equations, Journal of Optimization Theory and Applications 174 (2) (2017) 530-549.
dc.relation.referencesen[10] Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat. 15 2003-2016 (2010).
dc.rights.holder© Національний університет “Львівська політехніка”, 2017
dc.subjectConvection-diffusion problems
dc.subjectboundary layer
dc.subjectvariational iteration method
dc.subjectasymptotic expansion
dc.subjectauxiliary parameter
dc.titleNumerical solution of singularlyperturbed convection-diffusion equations
dc.typeConference Abstract

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