Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space

In this paper, we propose a new method to solve the forced Duffing equation with integral boundary conditions. Its exact solution is represented in the form of a series in the reproducing kernel space. The n-term approximation u _n (x) of the exact solution u(x) is proved to converge to the exact solution. Some numerical examples are displayed to demonstrate the accuracy of the present method.