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Error estimates for external approximation of ordinary differential equations and the superconvergence property. (English) Zbl 0664.65076
Superconvergence of approximate solutions of differential and integral equations is a well known phenomen. In this paper a class of external approximation is investigated. It is shown how superconvergence depends on the choice of a method from this class. The considerations are restricted to the case of the boundary value problems for ordinary differential equations of order 2m and to the external method generated by projections. A pointwise error estimate (via Green’s function) and an estimate in norm are obtained. Next superconvergence at the knot point is established for approximations generated by finite element subspaces and orthogonal projections.
Reviewer: Z.Schneider
MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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