scholarly journals An Analytical Computational Algorithm for Solving a System of Multipantograph DDEs Using Laplace Variational Iteration Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Mohamed S. M. Bahgat ◽  
A. M. Sebaq
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Computational Algorithm ◽  
Iteration Algorithm ◽  
Computational Results ◽  
Variational Iteration ◽  
Convergence Results ◽  
Delay Differential ◽  
High Degree ◽  
Symbolic Algorithm

In this research, an approximation symbolic algorithm is suggested to obtain an approximate solution of multipantograph system of type delay differential equations (DDEs) using a combination of Laplace transform and variational iteration algorithm (VIA). The corresponding convergence results are acquired, and an efficient algorithm for choosing a feasible Lagrange multiplier is designed in the solving process. The application of the Laplace variational iteration algorithm (LVIA) for the problems is clarified. With graphics and tables, LVIA approximates to a high degree of accuracy with a few numbers of iterates. Also, computational results of the considered examples imply that LVIA is accurate, simple, and appropriate for solving a system of multipantograph delay differential equations (SMPDDEs).

scholarly journals Convergence of Variational Iteration Method for Second-Order Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongliang Liu ◽  
Aiguo Xiao ◽  
Lihong Su
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Delay Differential Equations ◽  
Variational Iteration Method ◽  
Second Order ◽  
Effective Technique ◽  
Variational Iteration ◽  
Convergence Results ◽  
Delay Differential

This paper employs the variational iteration method to obtain analytical solutions of second-order delay differential equations. The corresponding convergence results are obtained, and an effective technique for choosing a reasonable Lagrange multiplier is designed in the solving process. Moreover, some illustrative examples are given to show the efficiency of this method.

scholarly journals Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mustafa Bahşi ◽  
Mehmet Çevik
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Taylor Series Expansion ◽  
Perturbation Parameter ◽  
Iteration Algorithm ◽  
Proportional Delay ◽  
Pantograph Equation ◽  
Functional Differential ◽  
Delay Differential

The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases.

Variational Iteration Method for Delay Differential Equations Using He’s Polynomials

2010 ◽  
Vol 65 (12) ◽  
pp. 1045-1048 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Ahmet Yildirim
Keyword(s):  
Applied Sciences ◽  
Signal Processing ◽  
Differential Equations ◽  
Iteration Method ◽  
Delay Differential Equations ◽  
Digital Images ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Delay Differential

January 21, 2010 In this paper, we apply the variational iteration method using He’s polynomials (VIMHP) for solving delay differential equations which are otherwise too difficult to solve. These equations arise very frequently in signal processing, digital images, physics, and applied sciences. Numerical results reveal the complete reliability and efficiency of the proposed combination.

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