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Analytical approximations for a conservative nonlinear singular oscillator in plasma physics. (English) Zbl 1267.34030

Summary: A modified variational approach and the coupled homotopy perturbation method with variational formulation are exerted to obtain periodic solutions of a conservative nonlinear singular oscillator in plasma physics. The frequency-amplitude relations for the oscillator which the restoring force is inversely proportional to the dependent variable are achieved analytically. The approximate frequency obtained using the coupled method is more accurate than the modified variational approach and ones obtained using other approximate methods and the discrepancy between the approximate frequency using this coupled method and the exact one is lower than 0.31% for the whole range of values of oscillation amplitude. The coupled method provides a very good accuracy and is a promising technique to a lot of practical engineering and physical problems.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
65L99 Numerical methods for ordinary differential equations
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