scholarly journals Novel approach to solve singularly perturbed boundary value problems with negative shift parameter

Heliyon ◽  
2021 ◽  
pp. e07497
Author(s):  
Gemechis File Duressa
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Shift Parameter ◽  
Negative Shift ◽  
Novel Approach

scholarly journals Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
F. Ghomanjani ◽  
A. Kılıçman ◽  
F. Akhavan Ghassabzade
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Time Interval ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Approximation Process ◽  
Negative Shift ◽  
Control Functions

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, intoksubintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degreenand determined Bezier curves on any subinterval byn+1control 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.

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