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Singular eigenvalue problems for second order linear ordinary differential equations

Árpád Elbert, Takaŝi Kusano, Manabu Naito (1998)

Archivum Mathematicum

We consider linear differential equations of the form ( p ( t ) x ' ) ' + λ q ( t ) x = 0 ( p ( t ) > 0 , q ( t ) > 0 ) ( A ) on an infinite interval [ a , ) and study the problem of finding those values of λ for which () has principal solutions x 0 ( t ; λ ) vanishing at t = a . This problem may well be called a singular eigenvalue problem, since requiring x 0 ( t ; λ ) to be a principal solution can be considered as a boundary condition at t = . Similarly to the regular eigenvalue problems for () on compact intervals, we can prove a theorem asserting that there exists a sequence { λ n } of eigenvalues such...

Strong convergence estimates for pseudospectral methods

Wilhelm Heinrichs (1992)

Applications of Mathematics

Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.

Superconvergence of external approximation for two-point boundary problems

Teresa Regińska (1987)

Aplikace matematiky

The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.

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