Periodic solutions of strongly quadratic non-linear oscillators by the elliptic Lindstedt-Poincare method

The elliptic Lindstedt-Poincare method is used/employed to study the periodic solutions of quadratic strongly non-linear oscillators of the form (x) double over dot + c(1)x + c(2)x(2) = epsilon f(x,. (x) over dot), 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) over dot) = mu(0) + mu(1)x - mu(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. (C) 1999 Academic Press.