Solution of the Duffing equation involving both integral and non-integral forcing terms

In this paper, a new iteration algorithm is proposed to solve the Duffing equation involving both integral and non-integral forcing terms in the reproducing kernel space. Its exact solution is represented in the form of series and the n  -term approximation un(x)un(x) of the exact solution u(x)u(x) is proved to converge to the exact solution. It is worthy to note that the method used in the paper can be applied for solving nonlinear differential equations.