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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 4 > No. 3


Solution of a Quadratic Non-Linear Oscillator by Elliptic Homotopy Averaging Method

PP: 313-317
A. M. El-Naggara, G. M. Ismail,
In this paper, the periodic solutions of a strongly quadratic nonlinear oscillator whose motion is described with the generalized Van der Pol equation are studied. A new method based on homotopy and averaging is employed to determine the limit cycle motion. Three types of quadratic nonlinearity are considered: the coefficients of the linear and quadratic terms are positive, the coefficient of the linear term is positive and that of the quadratic term is negative and the opposite case. Comparison with the numerical solutions is also presented, revealing that the present method leads to accurate solutions.

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