Collocation method for linear and nonlinear Fredholm and Volterra integral equations

Abstract

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterra integral equations, using the globally defined B-spline and auxiliary basis functions. The solution is collocated by cubic B-spline and then the integral equation is approximated by the 5-points Gauss–Turán quadrature formula with respect to the Legendre weight function. Combination of these two approaches is the main idea of this paper to reduce the cost of computation and complexity. The error analysis of proposed numerical method is studied theoretically. Numerical results are given to illustrate the efficiency of the proposed method. The results are compared with the results obtained by other methods to verify that this method is accurate and efficient.