Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations
Електронний науковий архів Науково-технічної бібліотеки Національного університету "Львівська політехніка"
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations
|
|
| Creator |
Erdogan, Fevzi
|
|
| Contributor |
Yuzuncu Yil University
|
|
| Subject |
The finite difference method
Appropriate piecewise-uniform Shishkin mesh |
|
| Description |
The purpose of this study is to present a uniform finite difference method for numerical solution of a initial value problem for quasi-linear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.
|
|
| Date |
2018-04-11T13:25:15Z
2018-04-11T13:25:15Z 2016 |
|
| Type |
Conference Abstract
|
|
| Identifier |
Erdogan F. Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations / Fevzi Erdogan // Litteris et Artibus : proceedings of the 6th International youth science forum, November 24–26, 2016, Lviv, Ukraine / Lviv Polytechnic National University. – Lviv : Lviv Polytechnic Publishing House, 2016. – P. 91–92. – Bibliography: 20 titles.
http://ena.lp.edu.ua:8080/handle/ntb/40260 |
|
| Language |
en
|
|
| Relation |
[1] R. Bellman, K.L. Cooke, Differential-Difference Equations, Academy Press, New York, 1963. [2] R.D. Driver, Ordinary and Delay Differential Equations, Belin-Heidelberg, New York, Springer, 1977. [3] A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford University Press, Oxford, 2003. [4] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. [5] S.N.Chow, J.Mallet-Paret, Singularly perturbed delaydifferential equations, in: J.Chandra, A.C.Scott (Eds.), Coupled Nonlinear Oscillators, North-Holland, Amsterdam, 1983, pp.7-12. [6] A. Longtin, J. Milton, Complex oscillations in the human pupil light reflex with mixed and delayed feedback, Math. Biosci. 90 (1988)183-199. [7] M.C. Mackey, L. Glass, Oscillation and chaos in physiological control systems, Science, 197(1977)287-289. [8] G.M. Amiraliyev, F. Erdogan, Uniform numerical method for singularly perturbed delay differential equations, J.Comput. Math. Appl. 53(2007)1251-1259. [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. [10] I.G. Amiraliyeva, Fevzi Erdogan, G.M.Amiraliyev, A uniform numerical method for dealing with a singularly perturbed delay initial value problem, Applied Mathematics Letters, 23,10(2010)1221-1225 . [11] S. Maset, Numerical solution of retarded functional differential equations as abstract Cauchy problems, J. Comput. Appl. Math. 161(2003)259-282. [12] B.J. MacCartin, Exponential fitting of the delayed recruitment/renewal equation. J. Comput. Appl. Math., 136(2001)343-356. [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. [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. [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. [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). [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). [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). [19] J.J.H. Miller, E. O’Riordan, G.I. Shishkin, Fitted Numerical Methods for Singular Perturbation Problems. Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific, Singapore, 1996. [20]T. Linss, M. Stynes, A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems, Appl. Numer. Math 31 (1999) 255-270.
|
|
| Format |
91-92
application/pdf |
|
| Coverage |
UA
Lviv |
|
| Publisher |
Lviv Polytechnic Publishing House
|
|