The optimal homotopy asymptotic method with application to modified Kawahara equation

Abstract

In this paper the optimal homotopy asymptotic method (OHAM) is introduced for obtaining the approximate solution of modified Kawahara equations. The OHAM results are compared with Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Exact solutions. The comparison of OHAM with these methods reveals that OHAM is very effective, reliable and efficient.ª 2014 Production and hosting by Elsevier B.V. on behalf of University of Bahrain.

Perturbation Solutions to Fifth Order Over-damped Nonlinear Systems

“…Akbar and Siddique [19] amplified the KBM method to obtain solutions of fifth order weakly nonlinear oscillatory systems. Also Optimal Homotopy Asymptotic Method [20][21][22] are developed for solving nonlinear evolutions equations.…”

“…computed by solution (22), in which and are computed by the equation 21with initial and For the above mentioned initial conditions, the perturbation results obtained by the solution (22) and the corresponding numerical results obtained by a fourth order Runge-Kutta method with a small time increment , are plotted in Fig. 1.…”

“…2. Perturbation solution plotted by solid line and numerical s Finally, for computed (22), in whichThe perturbation results obtained by the solution(22) and the corresponding numerical results obtained by a fourth order Runge-Kutta method with a small time increment correlation between the results is 0.999248…”

Application of homotopy analysis method to the solution of ninth order boundary value problems in AFTI-F16 fighters

“…Gepreel and Nofal (2015) used an improved optimal homotopy analysis method to solve partial fractional differential equations, with fractional derivative defined in Caputo sense. Ullah et al (2015) used the optimal homotopy asymptotic method (OHAM) for approximating the solution of modified Kawahara equations. Modified homotopy analysis method and homotopy perturbation transform method (Saha Ray and Sahoo, 2015) have been used to obtain the solution to time fractional coupled sine-Gordon equations.…”

An improved adaptation of homotopy analysis method

“…Siddiqi and Iftikhar [29] used the variational iteration method to approximate the solution of seventh order boundary value problems in terms of a convergent series. Hakeemullah et al [30] used the optimal homotopy asymptotic method (OHAM) for approximating the solution of modified Kawahara equations. The proposed method is numerically illustrated for the solutions of different higher order boundary value problems.…”