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Series solution for a delay differential equation arising in electrodynamics. (English) Zbl 1177.78059
Summary: 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.

MSC:
78M30 Variational methods applied to problems in optics and electromagnetic theory
78M25 Numerical methods in optics (MSC2010)
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