Applications of the Aboodh Transform and the Homotopy Perturbation Method to the Nonlinear Oscillators
DOI:
https://doi.org/10.26438/ijcse/v6i1.110Keywords:
Aboodh Transform, Homotopy Perturbation Method, Helmholtz-Duffing Oscillator, Van der Pol, Duffing Oscillator, Duffing-Van der Pol Oscillator, Approximate Analytical SolutionAbstract
In this paper, the differential equation of motion of the classical Helmholtz-Duffing oscillator, Van der Pol, Duffing oscillator and Duffing-Van der Pol oscillator equations have been solved analytically with the help of a new integral transform named Aboodh transform and homotopy perturbation method. By recasting the governing equations as nonlinear eigenvalue problems, we have obtained the excellent approximate analytical solution of the displacement and the relation between amplitude and angular frequency. We have also compared our results with exact numerical results graphically for few cases. Here, we have also demonstrated the sophistication and simplicity of this technique.
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