Approximate solution of nonlinear differential equations with convolution product nonlinearities

In this paper, a new iteration method is proposed to solve nonlinear problems. Special attention is paid to nonlinear differential equations with convolution product nonlinearities. The results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems. Furthermore, the first order of approximations are more accurate than perturbation solutions at high order of approximation.