| DC Field | Value | Language |
|---|
| dc.contributor.author | Erdogan, Fevzi | |
| dc.contributor.author | Sakar, Mehmet Giyas | |
| dc.coverage.temporal | 23–25 листопада 2017 року | |
| dc.coverage.temporal | 23–25 November, 2017 | |
| dc.date.accessioned | 2018-04-12T13:05:57Z | - |
| dc.date.available | 2018-04-12T13:05:57Z | - |
| dc.date.created | 2017-12-23 | |
| dc.date.issued | 2017-12-23 | |
| dc.identifier.citation | Erdogan 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.isbn | 978-966-941-108-2 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/40450 | - |
| dc.description.abstract | This 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.extent | 422-424 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Polytechnic Publishing House | |
| dc.relation.ispartof | Litteris et Artibus : матеріали, 2017 | |
| dc.relation.ispartof | Litteris et Artibus : proceedings, 2017 | |
| dc.subject | Singularly perturbed problems | |
| dc.subject | integrodifferential equation | |
| dc.subject | difference schemes | |
| dc.subject | uniformly convergent | |
| dc.title | A fitted numerical method for singularly perturbed integro differential equations with delay | |
| dc.type | Conference Abstract | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2017 | |
| dc.contributor.affiliation | Yuzuncu Yil University, Faculty of Sciences, Department of Mathematics, Van, Turkey | |
| dc.format.pages | 3 | |
| dc.identifier.citationen | Erdogan 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.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.citation.conference | 7th International youth science forum «Litteris et Artibus» | |
| dc.citation.journalTitle | Litteris et Artibus : матеріали | |
| dc.citation.spage | 422 | |
| dc.citation.epage | 424 | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| Appears in Collections: | Litteris et Artibus. – 2017 р.
|
