Author:
Debela Habtamu Garoma,Duressa Gemechis File
Abstract
AbstractIn this paper, accelerated fitted finite difference method for solving singularly perturbed delay differential equation with non-local boundary condition is considered. To treat the non-local boundary condition, Simpson’s rule is applied. The stability and parameter uniform convergence for the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter ε and mesh size h. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε-uniformly convergent for h ≥ ε where the classical numerical methods fails to give good result, and it also improves the results of the methods existing in the literature.
Publisher
Springer Science and Business Media LLC
Reference19 articles.
1. Longtin, A., Milton, J.: Complex oscillations in the human pupil light reflex with mixed and delayed feedback. Math. Biosci. 90, 183–199 (1988)
2. Glizer, V.Y.: Asymptotic analysis and solution of a finite-horizon H∝ control problem for singularly perturbed linear systems with small state delay. J. Optim. Theory Appl. 117, 295–325 (2003)
3. Culshaw, R.V., Ruan, S.: A delay differential equation model of HIV infection of C D4+ T-cells. Math. Biosci. 165, 27–39 (2000)
4. Els’gol’ts, E.L.: Qualitative methods in mathematical analysis in: translations of mathematical monographs, vol. 12. American Mathematical Society, Providence (1964)
5. Amiraliyev, G.M., Amiraliyev, I.G., Kudu, M.: A numerical treatment for singularly perturbed differential equations with integral boundary condition. Appl. Math. Comput. 185(1), 574–582 (2007)
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