Series solution for a delay differential equation arising in electrodynamics
Article first published online: 17 JUN 2009
Copyright © 2009 John Wiley & Sons, Ltd.
Communications in Numerical Methods in Engineering
Volume 25, Issue 11, pages 1084–1096, November 2009
How to Cite
Koçak, H. and Yıldırım, A. (2009), Series solution for a delay differential equation arising in electrodynamics. Commun. Numer. Meth. Engng., 25: 1084–1096. doi: 10.1002/cnm.1288
- Issue published online: 23 OCT 2009
- Article first published online: 17 JUN 2009
- Manuscript Accepted: 1 MAY 2009
- Manuscript Revised: 15 APR 2009
- Manuscript Received: 12 MAR 2009
- delay differential equations;
- the homotopy perturbation method;
- the variational iteration method
In this study, the pantograph equation is investigated using the homotopy perturbation and variational iteration methods. The pantograph equation is a delay differential equation that arises in quite different fields of pure and applied mathematics, such as number theory, dynamical systems, probability, mechanics and electrodynamics. The procedure of present methods are based on the search for a solution in the form of a series with easily computed components. Application of these techniques to this problem shows the rapid convergence of the sequence constructed by these methods to the exact solution. Moreover, this technique reduces the volume of calculations by not requiring discretization of the variables, linearization or small perturbations. Copyright © 2009 John Wiley & Sons, Ltd.