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Superconvergence and ultraconvergence of Newton–Cotes rules for supersingular integrals

✍ Scribed by Jin Li; Xiaoping Zhang; Dehao Yu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
756 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this article, the general (composite) Newton-Cotes rules for evaluating Hadamard finitepart integrals with third-order singularity (which is also called ''supersingular integrals'') are investigated and the emphasis is placed on their pointwise superconvergence and ultraconvergence. The main error of the general Newton-Cotes rules is derived, which is shown to be determined by a certain function S k (τ ). Based on the error expansion, the corresponding modified quadrature rules are also proposed. At last, some numerical experiments are carried out to validate the theoretical analysis.

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The superconvergence of the Newton–Cotes
The superconvergence of the Newton–Cotes rule for Cauchy principal value integrals
✍ Dongjie Liu; Jiming Wu; Dehao Yu 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 345 KB

We consider the general (composite) Newton-Cotes method for the computation of Cauchy principal value integrals and focus on its pointwise superconvergence phenomenon, which means that the rate of convergence of the Newton-Cotes quadrature rule is higher than what is globally possible when the singu