Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations. (English) Zbl 1197.34015

Barari, A.; Omidvar, M.; Ghotbi, Abdoul R.; Ganji, D. D.

Acta Appl. Math. 104, No. 2, 161-171 (2008).

The authors study the homotopy perturbation method (HPM) and variational iterative method (VIM) for nonlinear oscillator differential equations of the form \(u^{\prime\prime} + f (t, u, u^\prime ) = 0\). Some examples dealing with nonlinear initial value problems are solved by applying HPM and VIM. Comparing with the exact solutions, it is shown that the numerical solutions obtained by these methods are highly accurate.

Reviewer: Bashir Ahmad (Jeddah)

MSC:

34A45	Theoretical approximation of solutions to ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

homotopy perturbation method (HPM); variational iterative method (VIM); nonlinear oscillators; exact solution; van der Pol oscillator problem

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