Numerical solution of general nonlinear Fredholm-Volterra integral equations using Chebyshev ‎approximation

Subject Areas : International Journal of Industrial Mathematics

F. Fattahzadeh ¹ (Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.)

Received: 2016-02-06 Accepted : 2016-02-06 Published : 2016-01-01

Keywords: Nonlinear Fredholm-Volterra in, Chebyshev polynomials, Error analysis, Fast Fourier ‎Transform.‎,

Abstract :

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has lowest operation count in contrast to other early methods which use operational matrices (with huge number of operations) or involve intermediate numerical techniques for evaluating intermediate integrals which presented in integral equation or solve special case of nonlinear integral equations. Also rate of convergence are given. The numerical examples show the applicability and accuracy of the ‎method.‎