The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics

The pantograph equation is a delay differential equation which arises in quite different fields of pure and applied mathematics, such as number theory, dynamical systems, probability, mechanics and electrodynamics. In this work, the pantograph equation is investigated using the Adomian decomposition method and the convergence of the approach for this equation is established. The decomposition procedure of Adomian is based on the search for a solution in the form of a series with easily computed components. Application of the Adomian decomposition technique to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique reduces the volume of calculations by not requiring discretization of the variables, linearization or small perturbations.