Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra ( JLTA )2252-0201020420131213Approximate solution of fourth order differential equation in Neumann problem243254510025ENJ.RashidiniaSchool of Mathematics, Iran University of Science and Technology, Tehran, IranD.KalvandFaculty of Mathematics, Yerevan state University , Yerevan, ArmeniaL.TepoyanFaculty of Mathematics, Yerevan state University , Yerevan, ArmeniaJournal Article20130819Generalized solution on Neumann problem of the fourth order ordinary differential equation in space $W^2_alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when the solution is in classical form. Formulation of Quintic Spline Function has been derived and the consistency relations are given.Numerical method,based on Quintic spline approximation has been developed. Spline solution of the given problem has been considered for a certain value of $alpha$. Error analysis of the spline method is given and it has been tested by an example.http://jlta.iauctb.ac.ir/article_510025_d29a124b26073e7d4549702e0693dfa9.pdf