A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra-Fredholm integral equations

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.