Super Convergence Method for Solution of Higher Order Boundary Value Problems
Sh. Sharifi
Department of Mathematics and Statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
J. Rashidinia *
Department of Mathematics and Statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
*Author to whom correspondence should be addressed.
Abstract
A new O(h10) super convergence method based on B-spline of degree eight has been developed for solution of higher order boundary value problems. Our presented collocation method leads to optimal approximation, we describe the mathematical procedure in detail also analyze the convergence of the method. The obtained numerical results have been compared with results obtained by recent existing methods to verify the applicability and super convergence properties of the presented method numerically.
Keywords: Boundary value problem, B-spline collocation method, super convergence, Green's function