## SOLUTION OF THE VOLTERRA-FREDHOLM INTEGRAL EQUATIONS VIA THE BERNSTEIN POLYNOMIALS AND LEAST SQUARES APPROACH

## SOLUTION OF THE VOLTERRA-FREDHOLM INTEGRAL EQUATIONS VIA THE BERNSTEIN POLYNOMIALS AND LEAST SQUARES APPROACH

*N. Negarchi, K. Nouri*

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## Abstract

We develop a numerical scheme to solve a general category of Volterra- Fredholm integral equations. For this purpose, the Bernstein polynomials and their features have been used. We convert the main equation into a set of algebraic equations in which the coeâ€€cient matrix is obtained by the least squares approximation approach. The error analysis is given to corroborate the precision of the proposed method. Numerical results are presented to demonstrate the success of the scheme for solving integral equations.

## Keywords

Volterra-Fredholm integral equation, least squares approximation, Bernstein polynomials, Chebyshev-Gauss-Lobatto points.