Exact solution of system of multi-photograph type delay differential equations via new algorithm based on homotopy perturbation method

Abstract

A new algorithm is proposed in this paper to explain how the modified homotopy perturbation approach can be successfully implemented based on the Pade approximants and the Laplace trans-form in order to acquire the accurate solutions of a nonlinear system of multi-photograph delay differential equations. The method that has been suggested has the benefit of giving exact solutions, and it is simple to implement analytically on the issues that have been presented. Examples have been provided to demonstrate that this strategy may be utilized and is successful in its application. The results show that the method that was described could be used to solve many different types of differential equations.