  In this work, a new approach has been developed to obtain numerical solution
of linear Volterra type integral equations by obtaining asymptotic
approximation to solutions. Using the classical Bernoulli polynomials, a set of
orthonormal polynomials have been derived, and these orthonormal polynomials
have been used to form an operational matrix of integration which is has been
implemented to find numerical or exact solution of non-singular Volterra
integral equations. Two linear Volterra integral and two convolution integral
equations of second kind have been solved to demonstrate the effectiveness of
present method. Obtained approximate solutions have been compared with the
exact solutions for numerical values. High degree of accuracy of numerical
solutions has established the credibility of the present method.
