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The He’s amplitude-frequency formulation for solving strongly nonlinear oscillators differential equations. (English) Zbl 1387.34055

Summary: In this paper, He’s amplitude-frequency formulation (HAFF) is used to calculate the periodic solutions of nonlinear strongly oscillators. We find that HAFF works very well for the whole range of initial amplitudes and only one iteration leads to high accuracy of the solutions. Comparison of the result obtained using this method with other methods reveals that this modified method is very effective and convenient. The method is applied to three nonlinear differential equations.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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