DOI: 10.36347/sjpms

Pages: 87-95

In this paper, A numerical method based on an set of general, orthonormal Bernstein functions coupled with Block-Pulse Functions on the interval [0,1] to solve non linear Volterra integral equations of the second kind, numerically. First we introduced the proposed hybrid method, then we used it to transform the integral equations to the system of algebraic equations. The obtained numerical results of the proposed methods are compared with exact solution to show the convergence and advantages of the new method. the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra integral equations into some algebraic equations, the numerical example illustrate the efficiency and accuracy of this method. Keywords: Orthonormal Bernstein functions; Block-pulse functions; nonlinear Volterra integral equations; integration of the cross product, product matrix, coefficient matrix