AbstractIn this paper the stability and accuracy of an iterative method based on differential quadrature rules will be discussed. The method has already been proposed by the author in a previous work, where its good performance has been shown. Nevertheless, discussion about stability and accuracy remained open. An answer to this question will be provided in this paper, where the conditional stability of the method will be pointed out, in addition to an examination of the possible errors which arise under certain conditions. The discussion will be preceded by an overview of the method and its foundations, i.e. the differential quadrature rules, and followed by a numerical case which shows how the method behaves when applied to reduce continuous systems to two‐degree‐of‐freedom systems in the non‐linear range. In particular, here the case of oscillators coupled in non‐linear terms will be treated. The numerical results, used to draw Poincaré maps, will be compared with those obtained by using the Runge–Kutta method with a high precision goal. Copyright © 2003 John Wiley & Sons, Ltd.