Solving linear integral equations of the second kind with repeated modified trapezoid quadrature method

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermit interpolation [J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Second Edition, Springer-Verlag, 1993]. In this article we intend to make a quadrature method for solving the linear integral equations such as repeated trapezoid and repeated Simpson quadrature by using repeated modified trapezoid formula and by doing so, we solve the linear integral equations more accurately. For further information on quadrature methods see [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985] and [L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974]. 2006 Elsevier Inc. All rights reserved.