A Fourth-Order Collocation Scheme for Two-Point Interface Boundary Value Problems

Rakhim Aitbayev, Nazgul Oralbekovna Yergaliyeva

2014

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DOI 10.1155/2014/875013
Data confidence 70 medium
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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.