Superconvergence of external approximation for two-point boundary problems. (English) Zbl 0641.65064

The author considers the problem \(-u''+b(x)u=f(x),\) \(x\in \ell =[0,1]\), \(u(0)=u(1)=0\), where \(b(x)\geq \beta >0\), b,f\(\in L\) 2(\(\ell)\). The superconvergence properties of a certain external method (a generalization of the Galerkin method) for solving this problem is established. In the case when piecewise polynomial spaces are applied, it is proved that the rate of convergence of the approximate solution at the knot points can be exceed the global one.
Reviewer: D.Herceg


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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