The barycentric interpolation collocation method for a class of nonlinear vibration systems

Abstract

A nonlinear vibration system arises in physics. Besides its mathematical model, it is of great importance to have an accurate and reliable solution to the system. Though there are many analytical methods, such as the variational iteration method and the homotopy perturbation method, numerical approaches are rare. This paper suggests the barycentric interpolation collocation method to solve nonlinear oscillators. The Duffing equation is adopted as an example to elucidate the solution process. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.