Solving a singular system of two nonlinear ODEs

In this paper, a new method is given in order to solve a singular system of two nonlinear ordinary differential equations having multiple solutions, and we may give a special solution by imposing an additional condition. Representation of the exact solution is given in the form of series in the reproducing kernel space, its approximate solution is obtained by truncating the series. The error of the approximate solution is monotone decreasing in the sense of ∥·∥W2[0,1]∥·∥W2[0,1], and the intrinsic merit of the method given in the paper lies in its speedy convergence. Some numerical examples are studied to demonstrate the accuracy of the present method.