A fitted numerical method for singularly perturbed integro differential equations with delay

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dc.citation.conference7th International youth science forum «Litteris et Artibus»
dc.citation.epage424
dc.citation.journalTitleLitteris et Artibus : матеріали
dc.citation.spage422
dc.contributor.affiliationYuzuncu Yil University, Faculty of Sciences, Department of Mathematics, Van, Turkey
dc.contributor.authorErdogan, Fevzi
dc.contributor.authorSakar, Mehmet Giyas
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.coverage.temporal23–25 листопада 2017 року
dc.coverage.temporal23–25 November, 2017
dc.date.accessioned2018-04-12T13:05:57Z
dc.date.available2018-04-12T13:05:57Z
dc.date.created2017-12-23
dc.date.issued2017-12-23
dc.description.abstractThis study deals with the singularly perturbed initial value problems for a quasilinear first-order integrodifferential equations with delay. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the discrete solutions are uniformly convergent with respect to the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.
dc.format.extent422-424
dc.format.pages3
dc.identifier.citationErdogan F. A fitted numerical method for singularly perturbed integro differential equations with delay / Fevzi Erdogan, Mehmet Giyas Sakar // Litteris et Artibus : proceedings, 23–25 November, 2017. — Lviv : Lviv Polytechnic Publishing House, 2017. — P. 422–424. — (9th International academic conference «Computer science & engineering 2017» (CSE-2017)).
dc.identifier.citationenErdogan F. A fitted numerical method for singularly perturbed integro differential equations with delay / Fevzi Erdogan, Mehmet Giyas Sakar // Litteris et Artibus : proceedings, 23–25 November, 2017. — Lviv : Lviv Polytechnic Publishing House, 2017. — P. 422–424. — (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/40450
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] R. Bellman, K.L. Cooke, Differential-Difference Equations, Academy Press, New York, 1963.
dc.relation.references[2] R.D. Driver, Ordinary and Delay Differential Equations, Belin-Heidelberg, New York, Springer, 1977.
dc.relation.references[3] A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford University Press, Oxford, 2003.
dc.relation.references[4] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
dc.relation.references[5] S.N.Chow, J.Mallet-Paret, Singularly perturbed delay-differential equations, in: J.Chandra, A.C.Scott (Eds.), Coupled Nonlinear Oscillators, North-Holland, Amsterdam, 1983, pp.7-12.
dc.relation.references[6] A. Longtin, J. Milton, Complex oscillations in the human pupil light reflex with mixed and delayed feedback, Math. Biosci. 90 (1988)183-199.
dc.relation.references[7] M.C. Mackey, L. Glass, Oscillation and chaos in physiological control systems, Science, 197(1977)287-289.
dc.relation.references[8] G.M. Amiraliyev, F. Erdogan, Uniform numerical method for singularly perturbed delay differential equations, J.Comput. Math. Appl. 53(2007)1251-1259.
dc.relation.references[9] G.M. Amiraliyev, F. Erdogan, Difference schemes for a class of singularly perturbed initial value problems for delay differential equations, Numer. Algorithms, 52, 4(2009) 663-675.
dc.relation.references[10] I.G. Amiraliyeva, Fevzi Erdogan, G.M.Amiraliyev, A uniform numerical method for dealing with a singularly perturbed delay initial value problem, AppliedMathematics Letters, 23,10(2010)1221-1225.
dc.relation.references[11] S. Maset, Numerical solution of retarded functional differential equations as abstract Cauchy problems, J. Comput. Appl. Math. 161(2003)259-282.
dc.relation.references[12] B.J.MacCartin, Exponential fitting of the delayed recruitment/renewal equation. J. Comput. Appl. Math., 136(2001)343-356.
dc.relation.references[13] M.K. Kadalbajoo, K.K. Sharma, $\varepsilon- $uniform fitted mesh method for singularly perturbed differential difference equations with mixed type of shifts with layer behavior, Int. J. Comput. Math. 81 (2004)49-62.
dc.relation.references[14] C.G. Lange, R.M. Miura, Singular perturbation analysis of boundary-value problems for differential difference equations, SIAM J. Appl. Math. 42(1982)502-531.
dc.relation.references[15] H. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J. Math. Anal. Appl. 270(2002)143-149.
dc.relation.references[16] E. R. Doolan, J.J.H. Miller, and W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole, Press, Dublin, (1980).
dc.relation.references[17] P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E.O'Riordan and G.I.Shishkin, Robust Computational Techniques for Boundary Layers, Chapman- Hall/CRC, New York, (2000).
dc.relation.references[18] H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow Problems, Springer Verlag, Berlin, (1996).
dc.relation.references[19] G.M. Amiraliyev and H. Duru, A note on a parameterized singular perturbation problem, J.Comput. Appl. Math. 182 (2005) 233-242.
dc.relation.references[20] G.M. Amiraliyev, The convergence of a finite difference method on layer-adapted mesh for a singularly perturbed system, Applied Mathematics and Computation, 162,3(2005)1023-1034
dc.relation.referencesen[1] R. Bellman, K.L. Cooke, Differential-Difference Equations, Academy Press, New York, 1963.
dc.relation.referencesen[2] R.D. Driver, Ordinary and Delay Differential Equations, Belin-Heidelberg, New York, Springer, 1977.
dc.relation.referencesen[3] A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford University Press, Oxford, 2003.
dc.relation.referencesen[4] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
dc.relation.referencesen[5] S.N.Chow, J.Mallet-Paret, Singularly perturbed delay-differential equations, in: J.Chandra, A.C.Scott (Eds.), Coupled Nonlinear Oscillators, North-Holland, Amsterdam, 1983, pp.7-12.
dc.relation.referencesen[6] A. Longtin, J. Milton, Complex oscillations in the human pupil light reflex with mixed and delayed feedback, Math. Biosci. 90 (1988)183-199.
dc.relation.referencesen[7] M.C. Mackey, L. Glass, Oscillation and chaos in physiological control systems, Science, 197(1977)287-289.
dc.relation.referencesen[8] G.M. Amiraliyev, F. Erdogan, Uniform numerical method for singularly perturbed delay differential equations, J.Comput. Math. Appl. 53(2007)1251-1259.
dc.relation.referencesen[9] G.M. Amiraliyev, F. Erdogan, Difference schemes for a class of singularly perturbed initial value problems for delay differential equations, Numer. Algorithms, 52, 4(2009) 663-675.
dc.relation.referencesen[10] I.G. Amiraliyeva, Fevzi Erdogan, G.M.Amiraliyev, A uniform numerical method for dealing with a singularly perturbed delay initial value problem, AppliedMathematics Letters, 23,10(2010)1221-1225.
dc.relation.referencesen[11] S. Maset, Numerical solution of retarded functional differential equations as abstract Cauchy problems, J. Comput. Appl. Math. 161(2003)259-282.
dc.relation.referencesen[12] B.J.MacCartin, Exponential fitting of the delayed recruitment/renewal equation. J. Comput. Appl. Math., 136(2001)343-356.
dc.relation.referencesen[13] M.K. Kadalbajoo, K.K. Sharma, $\varepsilon- $uniform fitted mesh method for singularly perturbed differential difference equations with mixed type of shifts with layer behavior, Int. J. Comput. Math. 81 (2004)49-62.
dc.relation.referencesen[14] C.G. Lange, R.M. Miura, Singular perturbation analysis of boundary-value problems for differential difference equations, SIAM J. Appl. Math. 42(1982)502-531.
dc.relation.referencesen[15] H. Tian, The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag, J. Math. Anal. Appl. 270(2002)143-149.
dc.relation.referencesen[16] E. R. Doolan, J.J.H. Miller, and W. H. A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole, Press, Dublin, (1980).
dc.relation.referencesen[17] P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E.O'Riordan and G.I.Shishkin, Robust Computational Techniques for Boundary Layers, Chapman- Hall/CRC, New York, (2000).
dc.relation.referencesen[18] H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow Problems, Springer Verlag, Berlin, (1996).
dc.relation.referencesen[19] G.M. Amiraliyev and H. Duru, A note on a parameterized singular perturbation problem, J.Comput. Appl. Math. 182 (2005) 233-242.
dc.relation.referencesen[20] G.M. Amiraliyev, The convergence of a finite difference method on layer-adapted mesh for a singularly perturbed system, Applied Mathematics and Computation, 162,3(2005)1023-1034
dc.rights.holder© Національний університет “Львівська політехніка”, 2017
dc.subjectSingularly perturbed problems
dc.subjectintegrodifferential equation
dc.subjectdifference schemes
dc.subjectuniformly convergent
dc.titleA fitted numerical method for singularly perturbed integro differential equations with delay
dc.typeConference Abstract

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