Numerical Solutions of Fourth-Order, Two-Point IDEs Using RKHS Method

Abstract

This paper investigates approximate series solutions of fourth-order, two- point BVPs of Fredholm integro-differential equation using reproducing kernel Hilbert space method. The n-term approximation is obtained by truncating the series and proved that this approximation solution is converging to the exact solution. The error of the approximate solution is monotone decreasing in the sense of the norm of W 5 2 (0, 1). Moreover, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solutions and all its derivatives up to order four will be applicable. Results of numerical examples demonstrate that the method is quite accurate and efficient for the fourth-order, two- point BVPs of Fredholm integro-differential equations.