A Spectral Collocation Method With Piecewise Trigonometric Basis Functions for Nonlinear Volterra-Fredholm Integral Equations

Abstract

The aim of this paper is to investigate an efficient numerical method based on a novel shifted piecewise cosine basis for solving Volterra-Fredholm integral equations of the second kind. Using operational matrices of integration for the proposed basis functions, this integral equation is transformed into a system of nonlinear algebraic equations. The convergence and error analysis of the proposed method are studied. Some comparative results are provided to verify the efficiency of the presented method. (C) 2019 Elsevier Inc. All rights reserved.