A new modification of He's homotopy perturbation method for rapid convergence of nonlinear undamped oscillators

Abstract

In this paper we present a new efficient modification of the homotopy perturbation method with x 3 force nonlinear undamped oscillators for the first time that will accurate and facilitate the calculations. The He's homotopy perturbation method is modified by adding a term to linear operator depends on the equation and boundary conditions. We find that this modified homotopy perturbation method works very well for the wide range of time and boundary conditions for nonlinear oscillator. Only two or three iteration leads to high accuracy of the solutions. We then conduct a comparative study between the new modification and the homotopy perturbation method for strongly nonlinear oscillators. Numerical illustrations are investigated to show the accurate of the techniques. The new modified method accelerates the rapid convergence of the solution, reduces the error solution and increases the validity range. The new modification introduces a promising tool for many nonlinear problems.