A numerical solution of Volterra integral-algebraic equations using Bernstein polynomials

Abstract

The principal aim of this paper is to serve the numerical solution for a linear integralalgebraic equation (IAE) by using Bernstein polynomials. Employing of Bernstein polynomials, the system of integral equations is approximated by the Gaussian quadrature formula with respect to the Legendre weight function. The proposed method reduces the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical method. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods.