Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior

Abstract EN

We present a numerical method to solve boundary value problems (BVPs) for singularly perturbed differential-difference equations with negative shift.

In recent papers, the term negative shift has been used for delay.

The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations.

The approximation process is done in two steps.

First we divide the time interval, into k subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves.

We have chosen the Bezier curves as piecewise polynomials of degree n and determined Bezier curves on any subinterval by n+1 control points.

The proposed method is simple and computationally advantageous.

Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.