A Fourth-Order Collocation Scheme for Two-Point Interface Boundary Value Problems. (24th November 2014)

• Record Type: Journal Article
• Authors: Aitbayev, Rakhim; Yergaliyeva, Nazgul
• Other Names: Han Weimin Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2014(2014)
• Publication Date: 2014-11-24
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2014/875013
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : A fourth-order accurate orthogonal spline collocation scheme is formulated to approximate linear two-point boundary value problems with interface conditions. The coefficients of the differential operator may have jump discontinuities at the interface point, a nodal point of the scheme. Existence and uniqueness of the numerical solution are proved. Optimal order error estimates in the maximum norm are obtained, and a superconvergence property of the numerical solution in the maximal nodal norm is proved. Numerical results are presented confirming the theoretical estimates.