Spline Collocation for Volterra - Fredholm Integral Equations

The purpose of this paper is to develop a numerical method based on quintic B-spline to solve the linear and nonlinear Volterra-Fredholm integral equations. The solution is collocated by quintic B-spline and then the integrand is approximated by the Newton-Cotes formula. The arising system of linear or nonlinear algebraic equations can solve the linear combination coefficients appearing in the representation of the solution in spline basic functions. The error analysis of proposed numerical method is studied theoretically

Keywords:

Volterra-Fredholm , integral equations , quintic B-spline , Newton-Cotes formula , Error analysis