Approximate Solutions of Multi-Pantograph Type Delay Differential Equations Using Multistage Optimal Homotopy Asymptotic Method

Abstract

In this paper, a numerical procedure called multistage optimal homotopy asymptotic method (MOHAM) is introduced to solve multi-pantograph equations with time delay. It was shown that the MOHAM algorithm rapidly provides accurate convergent approximate solutions of the exact solution using only one term. A comparative study between the proposed method, the homotopy perturbation method (HPM) and the Taylor matrix method are presented. The obtained results revealed that the method is of higher accuracy, effective and easy to use.

Keywords

• approximate solutions
• multistage optimal homotopy asymptotic method (MOHAM)
• optimal homotopy asymptotic method (OHAM)
• pantograph equation
• series solution