Title: Application of Chebyshev polynomials for solving nonlinear Volterra-Fredholm integral equations system and convergence analysis
Abstract: n this paper, we solve the nonlinear Volterra-Fredholm integral equations system by using the Chebyshev polynomials. First we introduce the Chebyshev polynomials and approximate functions via their application. Then, we use Chebyshev polynomials as a collocation basis to change the nonlinear Volterra-Fredholm integral equations system to a system of nonlinear algebraic equations. Finally, the convergence analysis is considered, and numerical examples given to illustrate the efficiency of this method. Keywords: Volterra-Fredholm; System of integral equations; Chebyshev polynomials; Operational matrix