An approach based on statistical spline model for Volterra-Fredholm integral equations

In this paper, an approach based on statistical spline model (SSM) and colloca- tion method is proposed to solve Volterra-Fredholm integral equations. The set of collocation nodes is chosen so that the points yield minimal error in the nodal poly- nomials. Under some standard assumptions, we establish the convergence property of this approach. Numerical results on some problems are given to describe the intro- duced method. A comparison between the numerical results and those obtained from Lagrange and Taylor collocation methods demonstrates that the proposed method generates an approximate solution with minimal error.