PERIODIC SOLUTIONS OF STRONGLY QUADRATIC NON-LINEAR OSCILLATORS BY THE ELLIPTIC LINDSTEDT–POINCARÉ METHOD

Abstract The elliptic Lindstedt–Poincare method is used/employed to study the periodic solutions of quadratic strongly non-linear oscillators of the form x + c 1 x + c 2 x 2 = e f ( x , x ), in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical Lindstedt–Poincare method. The generalized Van de Pol equation with f ( x , x )= μ 0 + μ 1 x − μ 2 x 2 is studied in detail. Comparisons are made with the solutions obtained by using the Lindstedt–Poincare method and Runge–Kutta method to show the efficiency of the present method.