MMN-2978

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

**Elham Enteghami-Orimi**, University of Mazandaran, Faculty of Mathematical Sciences, 47416-95447, Babolsar, Iran,`e.enteghami@stu.umz.ac.ir`

**Azizollah Babakhani**, Babol Noshirvani University of Technology, Department of Mathematics, 4714871167, Babol, Iran,`babakhani@nit.ac.ir`

**Hassan Hosainzadeh**, University of Mazandaran, Faculty of Mathematical Sciences, 47416-95447, Babolsar, Iran,`hosinzadeh99@gmail.com`

## Abstract

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using Bernstein polynomials method. In this method, the system of integral equations is approximated by the Gauss quadrature formula with respect to the Legendre weight function. The proposed method reduce 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.

Vol. 22 (2021), No. 2, pp. 639-654

DOI: 10.18514/MMN.2021.2978