University of Tabriz Computational Methods for Differential Equations 2345-3982 4 1 2016 01 01 An approach based on statistical spline model for Volterra-Fredholm integral equations 30 42 5441 EN Amir Hossein Salehi Shayegan Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315 − 1618, Tehran, Iran Ali Zakeri Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315 − 1618, Tehran, Iran M. R. Peyghami Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315 − 1618, Tehran, Iran Journal Article 2016 06 20 ‎In this paper‎, ‎an approach based on statistical spline model (SSM) and collocation 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 polynomials‎. ‎Under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎Numerical results on some problems are given to describe the introduced 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. https://cmde.tabrizu.ac.ir/article_5441_a9657fe62ac81db659aa73c9a11cdc0f.pdf