The Analytic Solutions of Nonlinear Generalized Pantograph Differential Equations of Higher Order Via Coupled Adomian-Homotopy Technique

Abstract

     In this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it  gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives  better information over whole time interval. Finally, selected examples are given to show the accuracy, efficiency and effectiveness of this technique. This technique can be addressed and applied to other non-linear problems.