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

Rakhim Aitbayev | Zendy; Nazgul Oralbekovna Yergaliyeva | Zendy

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

Author(s) -

Rakhim Aitbayev,

Nazgul Oralbekovna Yergaliyeva

Publication year - 2014

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2014/875013

Subject(s) - mathematics , classification of discontinuities , uniqueness , superconvergence , boundary value problem , jump , mathematical analysis , norm (philosophy) , discontinuity (linguistics) , collocation (remote sensing) , finite element method , computer science , political science , law , thermodynamics , physics , quantum mechanics , machine learning

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

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