A new approach for solving multi-pantograph type delay differential equations

Abstract

In this paper, a modified procedure based on the residual power series method (RPSM) was implemented to achieve approximate solution with high degree of accuracy for a system of multi-pantograph type delay differential equations (DDEs). This modified procedure is considered as a hybrid technique used to improve the curacy of the standard RPSM by combining the RPSM, Laplace transform and Pade approximant to be a powerful technique that can be solve the problems directly without large computational work, also even enlarge domain and leads to very accurate solutions or gives the exact solutions which is consider the best advantage of this technique. Some numerical applications are illustrated and numerical results are provided to prove the validity and the ability of this technique for this type of important differential equation that appears in different applications in engineering and control system.