Generalized compound quadrature formulae for finite-part integrals |
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Authors: | DIETTELM KAI |
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Institution: |
Institut für Mathematik; Universität Hildesheini Marienburger Plarz 22, D-31141 Hildesheim, Germany
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Abstract: | Received on 31 July 1995. Revised on 19 August 1996. We investigate the error term of the dth degree compound quadratureformulae for finite-part integrals of the form where and p 1.We are mainly interested in error bounds of the form with best possible constants c. Itis shown that, for and n uniformlydistributed nodes, the error behaves as O(np–s–1for , p–1 <s d+1.In a previous paper we have shown that this is not true for As an improvement, we consider the case of non-uniformly distributednodes. Here, we show that for all p I and , an O(n–s) error estimate can be obtainedin theory by a suitable choice of the nodes. A set of nodeswith this property is staled explicitly. In practice, this gradedmesh causes stability problems which are computationally expensiveto overcome.
E-mail address: diethelm{at}informatik.uni-hildesheim.de |
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