Computation of an infinite integral using Romberg's method
type: Item
instance of: scholarly article
title: Computation of an infinite integral using Romberg's method
zbMATH Open document ID: 1071.65029
DOI: 10.1023/B:NUMA.0000040066.63826.46
published in: Numerical Algorithms
publication date: 2005-01-17T00:00:00Z
review text: The integral \[ g(a)= \int^t_0 [(\exp^x+ \exp^{-x})^a- \exp^{ax}- \exp^{-ax}]\,dx,\quad 0< a< 2 \] arises in a study of the total energy of crystals, where \(g(5/3)\) has been evaluated as 4.45. The aim of this paper is to show that a classical numerical computation, in this case with Romberg's method, leads to efficient and reliable computed results for any value of \(a\) if dynamical controls are used from the round-off error point of view. An estimation of the final round-off error and numerical examples are given.
reviewed by: Dumitru Acu
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65G20
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 2128418
zbMATH Keywords: Numerical validation
zbMATH Keywords: Romberg's method
zbMATH Keywords: CESTAC method
zbMATH Keywords: Numerical examples
zbMATH Keywords: round-off error
author: Fabienne Jézéquel
author: Jean-Marie Chesneaux
MaRDI profile type: Publication
full work available at URL: b:numa.0000040066.63826.46
OpenAlex ID: W2063492345
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description: scientific article; zbMATH DE number 2128418