He-Natural Homotopy Analysis Method for Solving Nonlinear Delay Differential Equations - Normah Maan , Aminu Barde (International Journal of Advanced Science and Technology, 2020)
Delay differential equations play a vital role in many areas of applied sciences. However,determining the solution of delay differential equations has become a difficult task, moreespecially the nonlinear type. Therefore, this research proposes a new analytical approach toobtain a solution of non-linear delay differential equations. The new approach is based on theNatural transform and Homotopy analysis method, which is called He-Natural HomotopyAnalysis Method (HeNHAM). The method gives solutions in the form of rapid convergence serieswhere the nonlinear terms are simply calculated using, He's polynomial. Different examples aregiven, and the results obtained indicate that the approach is efficient, reduces the computationalsizes, and avoid round-off of errors. The convergence analysis of the proposed method is alsoprovided.