Introduction:The theory and application of integral equation is an important subject within applied mathematics. There are several numerical approaches for solving linear Volterra integral equations of the second kind. Aim: In this paper , the Romberg's extrapolation is applied on quadrature method of numerical solution of linear Volterra integral equations of the second kind. Materials and Methods: An algorithm for new numerical solution calculated by Romberg's method is given. Results: The calculated solutions show more efficiency and accuracy with less computation than solution with quadrature method over more points of integration. Conclusion:The numerical results prove that the presented method is very effective and simple. The next advantage of this method respect to some other methods, is high accuracy and also convergence of the method which is very fast respect to similar method.
