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
In this paper, we presented an initial value approach for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right). By employing asymptotic power series expansion, the given singularly perturbed two-point boundary value problem is replaced by two first order initial value problems. To demonstrate the applicability of the present method three linear and two nonlinear problems with left end boundary layer are considered. It is observed that the present method approximates the exact solution very well.
In this paper, Adomian Decomposition Method with Discretization (ADMD) is applied to solve both linear and nonlinear initial value problems (IVP). Comparison with Adomian Decomposition Method (ADM) is presented. To illustrate the efficiency and accuracy of the method, five examples are considered. The result shows that ADMD is more efficient and accurate than ADM. Index Terms-Decomposition method, Adomian polynomial, initial value problems, infinite series.
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