Computational Treatment of First Order Delay Differential Equations Using Hybrid Extended Second Derivative Block Backward Differentiation Formulae

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
C. Chibuisi ◽  
Bright Okore Osu ◽  
C. Olunkwa ◽  
S. A. Ihedioha ◽  
S. Amaraihu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Derivative ◽  
Delay Term ◽  
First Order ◽  
Block Form ◽  
Collocation Approach ◽  
Backward Differentiation Formulae ◽  
Delay Differential ◽  
Step Number

This paper considers the computational solution of first order delay differential equations (DDEs) using hybrid extended second derivative backward differentiation formulae method in block form without the implementation of interpolation techniques in estimating the delay term. By matrix inversion approach, the discrete schemes were obtained through the linear multistep collocation approach from the continuous form of each step number which after implementation strongly revealed the convergence and region of absolute stability of the proposed method. Computational results are presented and compared to the exact solutions and other existing method to demonstrate its efficiency and accuracy.

scholarly journals Solving Delay Differential Equations Using Reformulated Block Backward Differentiation Formulae Methods

2019 ◽  
pp. 1-15
Author(s):  
U. W. Sirisena ◽  
S. Y. Yakubu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Approximate Solutions ◽  
Delay Argument ◽  
Block Form ◽  
One Step ◽  
Backward Differentiation Formulae ◽  
The Stability ◽  
Delay Differential ◽  
Step Number

In this paper, the conventional backward differentiation formulae methods for step numbers k = 3 and 4 were reformulated by shifting them one-step backward to produce two and three approximate solutions respectively, in a step when implemented in block form. The derivation of the continuous formulations of the reformulated methods were carried out through multistep collocation method by matrix inversion technique. The discrete schemes were deduced from their respective continuous formulations. The convergence analysis of the discrete schemes were discussed. The stability analysis of these schemes were ascertained and the P- and Q-stability were also investigated. When the discrete schemes were implemented in block form to solve some first order delay differential equations together with an accurate and efficient formula for the solution of the delay argument, it was observed that the results obtained from the schemes for step number k = 4 performed slightly better than the schemes for step number k = 3 when compared with the exact solutions. More so, on comparing these methods with some existing ones, it was observed that the methods derived performed better in terms of accuracy.

scholarly journals Computation of First order Delay Differential Equations via Simpson Block Method

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Ridwanulahi I Abdulganiy ◽  
Olusheye A Akinfenwa ◽  
Osaretin E Enobabor ◽  
Blessing I Orji ◽  
Solomon A Okunuga
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Step Width ◽  
Block Method ◽  
Delay Term ◽  
First Order ◽  
Collocation Technique ◽  
Delay Differential

A family of Simpson Block Method (SBM) is proposed for the numerical integration of Delay Differential Equations (DDEs). The methods are developed through multistep collocation technique using constant step width. The convergence and accuracy of the methods are established through some standard DDEs in the reviewed literature. Keywords— Block Method, Collocation Technique, Delay Term, Delay Differential Equation, Self Starting.   

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

scholarly journals First Order Nonlinear Neutral Delay Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 347-349 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Nonoscillatory Solutions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

scholarly journals Oscillation of Nonlinear First Order Neutral Differential Equations

2007 ◽  
Vol 4 (3) ◽  
pp. 485-490
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Integral Conditions ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

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