He-Natural Homotopy Analysis Method for Solving Nonlinear Delay Differential Equations

Abstract

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, more
especially the nonlinear type. Therefore, this research proposes a new analytical approach to
obtain a solution of non-linear delay differential equations. The new approach is based on the
Natural transform and Homotopy analysis method, which is called He-Natural Homotopy
Analysis Method (HeNHAM). The method gives solutions in the form of rapid convergence series
where the nonlinear terms are simply calculated using, He's polynomial. Different examples are
given, and the results obtained indicate that the approach is efficient, reduces the computational
sizes, and avoid round-off of errors. The convergence analysis of the proposed method is also
provided.