Generalized Gaussian quadratures for integrals with logarithmic singularity

Milovanović, Gradimir V.

doi:10.2298/fil1604111m

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2020

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“…In the other words, these rules are exact for each f (x) = p(x) + q(x) log x, where p, q ∈ P n−1 , so that they can calculate integrals with a sufficient accuracy, regardless of whether their integrands contain a logarithmic singularity, or they do not. For a similar approach for integrals on the finite intervals see [12] and [14].…”

Section: Introductionmentioning

confidence: 99%

Weighted quadrature formulas for semi-infinite range integrals

Milovanović

2015

J. Numer. Anal. Approx. Theory

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Weighted quadrature formulas on the half line \((a,+\infty)\), \(a>0\), for non-exponentially decreasing integrands are developed. Such \(n\)-point quadrature rules are exact for all functions of the form \(x\mapsto x^{-2}P(x^{-1})\), where \(P\) is an arbitrary algebraic polynomial of degree at most \(2n-1\). In particular, quadrature formulas with respect to the weight function \(x\mapsto w(x)=x^\beta\log^m x\) (\(0\le \beta<1\), \(m\in \mathbb{N}_0\)) are considered and several numerical examples are included.

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Section: Introductionmentioning

confidence: 99%