Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

Abstract

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation

“…Hence, few approaches have been implemented in solving them such as approximation, asymptotic solutions, numerical method, and graphical approaches. In recent times, Anakira et al employed the Optimal Homotopy Asymptotic Method (OHAM) in solving linear and nonlinear DDE [2] while Alomari et al used the Homotopy Analysis Method (HAM) to find the solution for DDE [3]. Among all these methods applied to solve differential equations, one of them is the variational iteration method (VIM) which was firstly initiated by Ji-Huan He which could be seen throughout [4][5][6][7][8].…”

An Accurate Approximate Solutions of Multipoint Boundary Value Problems

“…This procedure give us with a convenient way to control the convergence of approximation series and demonstrates its validity and potential efficiency to solve a wide class of problems in applied science and engineering and also valid for small parameters. In the last few years, OHAM and its modifications has been applied successfully to solve many types of differential equations [12,13,14,15,16,17,18,19,20,21].…”

An optimal method for approximating the delay differential equations of noninteger order

“…Accordingly, for such differential equations, we have to consider some direct and iterative methods. Some of these techniques used by scholars include the finite difference method [27], the homotopy perturbation method (HPM) [28,29], the differential transform method (DTM) [30,31], Adomian's decomposition method (ADM) [31], the optimal homotopy asymptotic method (OHAM) [32], the homotopy analysis method (HAM) [33][34][35], the variational iteration method (VIM) [36], and so on [37][38][39][40].…”