Simulating non-linear coupled oscillators by an iterative differential quadrature method

An iterative method based on differential quadrature rules is proposed as a new unified frame of resolution for non-linear two-degree-of-freedom systems. Dynamical systems with Duffing-type non-linearity have been considered. Differential quadrature rules have been applied with a careful distribution of sampling points to reduce the governing equation of motion to two second-order non-linear, non-autonomous ordinary differential equations and to solve the time-domain problem. The time domain of the problem is discretized by means of time intervals, with the same distribution of sampling points used to discretize the space domain (which can be seen as a single interval). It will be shown that accurate solutions depend not only on the choice of the distribution of sampling points, but also on the length of the time interval one refers to in the computations. The numerical results, utilized to draw Poincaré maps, are successfully compared with those obtained using the Runge-Kutta method.