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)u(x) and approximate solution un(x)un(x) are represented in terms of series. For any initial function u1(x)∈W23[0,1], we prove un(x)→u(x)un(x)→u(x), un′(x)→u′(x), un″(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.