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Supraconvergence of a finite difference scheme for solutions in \(H^S(0,L)\). (English) Zbl 1087.65070

The paper deals with the numerical analysis of linear two-point boundary value problems. The authors study the convergence properties of a centered finite difference scheme. The main statement is a supraconvergence theorem showing second order convergence for solutions in the Sobolov space \(H^3\). The main idea in the proof is to recognize that the finite difference scheme is equivalent to a fully discrete linear finite element method. Finally, the proposed order of convergence of the numerical scheme applied to a test example is shown.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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