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

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...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2015, Vol.2015 (2015), p.22-31-002
Main Authors: Bahsi, M. Mustafa, Cevik, Mehmet
Format: Article
Language:English
Subjects:
Algorithms
Delay
Differential equations
Iterative methods
Mathematical analysis
Mathematical models
Pantographs
Perturbation (Mathematics)
Perturbation methods
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2015/139821