A new method for solving a class of singular two-point boundary value problems

In this paper, we present a new method for solving a class of singular two-point boundary value problems for certain ordinary differential equations having singular coefficients. The exact solution u(x)u(x) is represented in the form of series in the reproducing kernel space. In the mean time, the n  -term approximate solution un(x)un(x) is obtained by solving a linear system of equations and is proved to converge to the exact solution. This method can avoid the Gram–Schmidt orthogonalization process, so as to improve the precision and decrease consumedly the runtime when the number of knots is the same, especially when the number of knots is large. It is efficiently applied to solve some model problems with the comparison between the numerical solutions and the exact solutions. The high precision of this method is demonstrated by the numerical examples.