University of Tabriz Computational Methods for Differential Equations 2345-3982 9 1 2021 01 01 Quintic Spline functions and Fredholm integral equation 211 224 9948 10.22034/cmde.2019.31983.1492 EN Khosrow Maleknejad School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran. Jalil Rashidinia School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran. Hamed Jalilian School of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran. Journal Article 2019 02 09 A new six order method developed for the approximation Fredholm integral equation of the second kind. This method is based on the quintic spline functions (QSF). In our approach, we first formulate the Quintic polynomial spline then the solution of integral equation approximated by this spline. But we need to develop the end conditions which can be associated with the quntic spline. To avoid the reduction accuracy, we formulate the end condition in such a way to obtain the band matrix and also to obtain the same order of accuracy. The convergence of the method is discussed by using matrix algebra. Finally, four test problems have been used for numerical illustration to demonstrate the practical ability of the new method. https://cmde.tabrizu.ac.ir/article_9948_d01f26099943ca195f6b0f7a0a05fbbd.pdf