New algorithm for the numerical solution of the integro-differential equation with an integral boundary condition

In this paper, a sequence of approximate solution converging uniformly to the exact solution for a class of integro-differential equation with an integral boundary condition arising in chemical engineering, underground water flow and population dynamics and other field of physics and mathematical chemistry is obtained by using an iterative method. Its exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation u _n (x) is proved to converge to the exact solution u(x). Moreover, the first derivative of u _n (x) is also convergent to the first derivative of u(x).