A Natural Homotopy Analysis Method for Nonlinear Delay Differential Equations

Delay differential equation (DDEs) is a type of functional differential equation arising in numerous applications from different areas of studies, for example biology, engineering population dynamics, medicine, physics, control theory, and many others. However, determining the solution of delay differential equations has become a difficult task more especially the nonlinear type. Therefore, this work proposes a new analytical method for solving non-linear delay differential equations. The new method is combination of Natural transform and Homotopy analysis method. The approach gives solutions inform of rapid convergence series where the nonlinear terms are simply computed using He's polynomial. Some examples are given, and the results obtained indicate that the approach is efficient in solving different form of nonlinear DDEs which reduces the computational sizes and avoid round-off of errors.