University of TabrizComputational Methods for Differential Equations2345-39829120210101Quintic Spline functions and Fredholm integral equation211224994810.22034/cmde.2019.31983.1492ENKhosrowMaleknejadSchool of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran.JalilRashidiniaSchool of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran.0000-0002-9177-900XHamedJalilianSchool of Mathematics, Iran University of Science and Technology Narmak, Tehran 16844, Iran.Journal Article20190209A 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