ENHANCED EFFICIENT ANALYTICAL APPROACH FOR NON-LINEAR SYSTEM OF DDES

Abstract

Delay differential equations (DDEs) have been used as fundamental tools in describing models in Sciences, engineering, and many other fields. These models in turn play a vital role in human life setting.  However, analytical treatment of such models described by various forms of nonlinear systems of DDEs are very difficult to handle due to the lack of direct and simplified approach of evaluating the nonlinear terms. In this work, an efficient analytical approach for nonlinear systems of DDEs has been enhanced by modifying the He's polynomial. The aim is to ease the computational difficulties of nonlinear terms for the system of DDEs. The approach is applied to obtain approximate analytical solution of famous models from mathematical physics and biology. Therefore, the method provides solution of these models in form of polynomial series. Moreover, using an optimum value of auxiliary parameters the more precise approximation is obtained from only three iterations number of terms. Figures are used to illustrate the correctness of the result based on the residual error functions. Hence, the technique provides an easiest and straightforward means of solving these models analytically. Thus, it can also be used in obtaining solutions of other types of DDEs.