<![CDATA[<B>Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations</B>]]>

Abstract

Abstract. In this paper, the boundary value problems for second order singularly perturbed delay differential equations are treated. A generic numerical approach based on finite difference is presented to solve such boundary value problems. The stability and convergence analysis of the method is studied. The solution of the boundary value problems when delay is zero, exhibits layer behavior. Here, the study focuses on the effect of delay on the boundary layer behavior of the solution via numerical approach. The effect of the delay on the boundary layer behavior of the solution is shown by carrying out some numerical experiments.Mathematical subject classification: G.1.7.

An abstract framework in the numerical solution of boundary value problems for neutral functional differential equations

“…BVPs for non-neutral delay differential equations [8,12,28,29,37,38,49,52] BVPs for non-neutral differential equations with deviating arguments [1,3,[9][10][11]19,20,50,51,53] BVPs for non-neutral differential equations with a state-dependent deviating argument θ(t, y(t)) [4] BVPs for non-neutral singularly perturbed differential equations with deviating arguments [31][32][33][34][35] BVPs for the determination of periodic solutions of non-neutral delay differential equations [15,16,18,39,54] BVPs for the determination of periodic solutions of non-neutral delay differential equations with a state-dependent delay [40] BVPs for the determination of periodic solutions of non-neutral differential equations with deviating arguments [6,7] BVPs for non-neutral Fredholm integro-differential equations [21,22,45] BVPs for non-neutral Fredholm integro-differential equations with weakly singular kernels [46][47][48] BVPs for non-neutral Volterra integro-differential equations [23] BVPs for the determination of periodic solutions of neutral delay differential equations [5,17] BVPs for neutral differential equations with st...…”

Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by Ε-Approximate Fixed-Point Method

“…Downloaded by [New York University] at 11:11 08 June 2015 4 Numerical Experiments Example 1. Consider the following boundary value problem ( [5]):…”

A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient

“…But in the recent years, there has been growing interest in this area. The authors of [12,6,16,1,2] suggested some numerical methods for singularly perturbed delay differential equations with continuous data. Recently few authors in [20,21,17] suggested some numerical method for singularly perturbed delay differential equations with discontinuous data.…”