New algorithm for second-order boundary value problems of integro-differential equation

This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space. The analytical solution u ( x ) and approximate solution u n ( x ) are represented in terms of series. For any initial function u 1 ( x ) ∈ W 2 3 [ 0 , 1 ] , we prove u n ( x ) → u ( x ) , u n ′ ( x ) → u ′ ( x ) , u n ″ ( x ) → u ″ ( x ) ( n → ∞ ) . Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.