This paper presents a Chebyshev-Gauss collocation method to determine an approximate solution to the initial value problems of ordinary differential equations. We propose an algorithm to solve an ordinary differential equation on a singleinterval domain and extend the algorithm to a multi-interval domain. We then generalize the algorithm to the system of ordinary differential equations including the Hamiltonian systems. Numerical results show that the proposed method gives a spectral accuracy. The comparison of our method to some related work is provided to show the accomplishment of the method.
