This review is an elementary introduction to the concepts of the recently developed
asymptotic methods and new developments. Particular attention is paid throughout the …

The homotopy perturbation method is extremely accessible to non-mathematicians and
engineers. The method decomposes a complex problem under study into a series of simple …

This paper deals with the nonlinear oscillations of a particle which moves on a rotating
parabola. An analytic approximate technique, namely optimal homotopy asymptotic method …

Geng and Cai suggested a modified He's frequency–amplitude formulation for nonlinear
oscillators (Geng and Cai 2007 Eur. J. Phys. 28 923–31). We point out the accuracy of both …

The Painlevé equations were discovered by Painlevé, Gambier and their colleagues during
studying a nonlinear second‐order ordinary differential equation. The six equations which …

This paper investigates the forced Duffing equation with integral boundary conditions. Its
approximate solution is developed by combining the homotopy perturbation method (HPM) …

In this paper we propose a reliable algorithm for the solution of nonlinear oscillators. Our
algorithm is based upon the homotopy perturbation method (HPM), Laplace transforms, and …

In this paper an analytical technique, called the optimal homotopy perturbation method
(OHPM), is employed to study the nonlinear behaviour of an electrical machine modelled as …

In this paper, based on homotopy perturbation method (HPM) and reproducing kernel
method (RKM), a new method is presented for solving nonlinear systems of second order …

He’s frequency–amplitude formulation for the Duffing harmonic oscillator - ScienceDirect
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