Solving a class of singular boundary value problems in the reproducing kernel Hilbert space

A method for solving singular boundary value problems with linear boundary conditions is presented. First a reproducing kernel Hilbert space with linear boundary conditions arising in problems we will concern is constructed. Then the exact solution of singular boundary value problem is represented in the form of series in the reproducing kernel Hilbert space. In the mean time, the approximate solution un(x) can be obtained by the n-term intercept of the exact solution u(x).The solution we obtain has its own advantages. For example, once the solution has been computed, the information on entire interval is available. This is particularly significant when the solution of the boundary value problem is required at various locations on the entire interval. Two numerical examples are studied to demonstrate the accuracy of the present method. Result obtained by the method is found to be in good agreement with the exact solution.