Solution of the Volterra-Fredholm integral equations via the Bernstein polynomials and least squares approach

Abstract

We develop a numerical scheme to solve a general category of VolterraFredholm 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 coefficient 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.