Numerical Solution of Second-Order Linear Delay Differential and Integro-Differential Equations by Using Taylor Collocation Method

2019 ◽  
Vol 17 (09) ◽  
pp. 1950070
Author(s):  
A. Bellour ◽  
M. Bousselsal ◽  
H. Laib
Keyword(s):  
Differential Equations ◽  
Numerical Approach ◽  
Second Order ◽  
Constant Delay ◽  
Numerical Examples ◽  
Order Linear ◽  
Linear Delay ◽  
Taylor Polynomials ◽  
Delay Differential ◽  
Collocation Solution

The main purpose of this work is to provide a numerical approach for linear second-order differential and integro-differential equations with constant delay. An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution [Formula: see text] for approximating the solution of second-order linear DDEs and DIDEs. It is shown that this algorithm is convergent. Some numerical examples are included to demonstrate the validity of this algorithm.

Oscillations of second order linear delay differential equations

1988 ◽  
Vol 27 (1-3) ◽  
pp. 109-123 ◽  
Author(s):  
M.R.S. Kulenvić ◽  
G. Ladas ◽  
Y.G. Sficas
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Order Linear ◽  
Linear Delay ◽  
Delay Differential

scholarly journals Second-Order Delay Differential Equations to Deal the Experimentation of Internet of Industrial Things via Haar Wavelet Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yongtao Xuan ◽  
Rohul Amin ◽  
Fakhar Zaman ◽  
Zohaib Khan ◽  
Imad Ullah ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Approach ◽  
Haar Wavelet ◽  
Second Order ◽  
Algebraic Equations ◽  
Elimination Algorithm ◽  
Collocation Points ◽  
Delay Differential ◽  
Mean Square Errors

In this article, an efficient numerical approach for the solution of second-order delay differential equations to deal with the experimentation of the Internet of Industrial Things (IIoT) is presented. With the help of the Haar wavelet technique, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for various collocation points. The results show that the Haar wavelet method is an effective method for solving delay differential equations of second order. The convergence rate is also measured for various collocation points, which is almost equal to 2.

Oscillation criteria for second-order half-linear delay differential equations with mixed neutral terms

2019 ◽  
Vol 69 (5) ◽  
pp. 1117-1126
Author(s):  
Said R. Grace ◽  
John R. Graef ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Linear Delay ◽  
Delay Differential

Abstract This article concerns the oscillatory behavior of solutions to second-order half-linear delay differential equations with mixed neutral terms. The authors present new oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are illustrated with examples.

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