Reliable treatment for solving boundary value problems of pantograph delay differential equation

This work presents an accurate and reliable treatment of the pantograph equation, which is a delay differential equation that appears in many scientific applications. The Adomian decomposition method and the variational iteration method will be used to carry out this work. Both the Adomian decomposition method and the variational iteration method provide convergent series solutions for linear and nonlinear differential equations. We conduct a comparative study between the two methods by highlighting the specific features of each method. Four linear and nonlinear pantograph equations will be investigated to support this work. The power of the two methods is confirmed.