A novel method for solving a class of second order nonlinear differential equations with finitely many singularities

In this paper, a novel method is presented for solving a class of second order nonlinear differential equations with finitely many singularities in the reproducing kernel space W23[a,b]. The exact solution u(x)u(x) is represented in the form of series. In the mean time, the nn term approximate solution un(x)un(x) of u(x)u(x) is proved to converge to the exact solution in the sense of norm, the error of the numerical solution is monotonically decreasing with the increase of nn. Numerical examples demonstrate the accuracy of the present method. Numerical results verify that the proposed method is effective and simple for this kind of problems.