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

Abstract

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 W 2 3 [ a , b ] . The exact solution u ( x ) is represented in the form of series. In the mean time, the n term approximate solution u n ( x ) of 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 n . 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.