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An Asymptotic-Fitted Method for Solving Singularly Perturbed Delay Differential Equations

DOI: 10.4236/am.2012.38132, PP. 895-902

Keywords: Asymptotic-Fitted Scheme, Delay-Differential Equations, Singular Perturbation, Boundary Layer

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Abstract:

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equation, we introduced a fitting parameter and determined its value using the theory of singular Perturbation; O’Malley [1]. The three term recurrence relation obtained is solved using Thomas algorithm. The applicability of the method is tested by considering five linear problems (two problems on left layer and one problem on right layer) and two nonlinear problems.

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