Modification of the Euler quadrature formula for functions with a boundary-layer component

The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying th...

Full description

Saved in:
Bibliographic Details
Published in:Computational mathematics and mathematical physics 2014-10, Vol.54 (10), p.1489-1498
Main Author: Zadorin, A. I.
Format: Article
Language:English
Subjects:
Boundaries
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Derivatives
Error analysis
Eulers equations
Interpolation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Polynomials
Quadratures
Studies
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c301t-8728ab1ac452be32e031e8f121a421dc4fdd872ec6ef0650e959fd9d201e11bd3
container_end_page 1498
container_issue 10
container_start_page 1489
container_title Computational mathematics and mathematical physics
container_volume 54
creator Zadorin, A. I.
description The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.
doi_str_mv 10.1134/S0965542514100078
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1629341760</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3466463661</sourcerecordid><originalsourceid>FETCH-LOGICAL-c301t-8728ab1ac452be32e031e8f121a421dc4fdd872ec6ef0650e959fd9d201e11bd3</originalsourceid><addsrcrecordid>eNp1kD9PwzAUxC0EEqXwAdgssbAE_JzYTUZU8U8qYgAWlsixn2mqNG7tWKjfHkdlQCCmG-53p_eOkHNgVwB5cf3CKilEwQUUwBiblQdkAkKITErJD8lktLPRPyYnIawYA1mV-YS8PznT2laroXU9dZYOS6S3sUNPt1EZr4bokVrn17FTo1Ibez3CgX62w5Iq2rjYG-V3Wad2KabdeuN67IdTcmRVF_DsW6fk7e72df6QLZ7vH-c3i0znDIasnPFSNaB0IXiDOUeWA5YWOKiCg9GFNSYxqCVaJgXDSlTWVIYzQIDG5FNyue_deLeNGIZ63QaNXad6dDHUIHmVFzCTLKEXv9CVi75P1yUKinyWhuOJgj2lvQvBo603vl2nD2tg9bh2_WftlOH7TEhs_4H-R_O_oS8me4Fh</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1614370782</pqid></control><display><type>article</type><title>Modification of the Euler quadrature formula for functions with a boundary-layer component</title><source>ABI/INFORM Global</source><source>Springer Nature</source><creator>Zadorin, A. I.</creator><creatorcontrib>Zadorin, A. I.</creatorcontrib><description>The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.</description><identifier>ISSN: 0965-5425</identifier><identifier>EISSN: 1555-6662</identifier><identifier>DOI: 10.1134/S0965542514100078</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Boundaries ; Computational mathematics ; Computational Mathematics and Numerical Analysis ; Construction ; Derivatives ; Error analysis ; Eulers equations ; Interpolation ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Polynomials ; Quadratures ; Studies</subject><ispartof>Computational mathematics and mathematical physics, 2014-10, Vol.54 (10), p.1489-1498</ispartof><rights>Pleiades Publishing, Ltd. 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c301t-8728ab1ac452be32e031e8f121a421dc4fdd872ec6ef0650e959fd9d201e11bd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/1614370782?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,11688,27924,27925,36060,36061,44363</link.rule.ids></links><search><creatorcontrib>Zadorin, A. I.</creatorcontrib><title>Modification of the Euler quadrature formula for functions with a boundary-layer component</title><title>Computational mathematics and mathematical physics</title><addtitle>Comput. Math. and Math. Phys</addtitle><description>The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.</description><subject>Boundaries</subject><subject>Computational mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Construction</subject><subject>Derivatives</subject><subject>Error analysis</subject><subject>Eulers equations</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Quadratures</subject><subject>Studies</subject><issn>0965-5425</issn><issn>1555-6662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>M0C</sourceid><recordid>eNp1kD9PwzAUxC0EEqXwAdgssbAE_JzYTUZU8U8qYgAWlsixn2mqNG7tWKjfHkdlQCCmG-53p_eOkHNgVwB5cf3CKilEwQUUwBiblQdkAkKITErJD8lktLPRPyYnIawYA1mV-YS8PznT2laroXU9dZYOS6S3sUNPt1EZr4bokVrn17FTo1Ibez3CgX62w5Iq2rjYG-V3Wad2KabdeuN67IdTcmRVF_DsW6fk7e72df6QLZ7vH-c3i0znDIasnPFSNaB0IXiDOUeWA5YWOKiCg9GFNSYxqCVaJgXDSlTWVIYzQIDG5FNyue_deLeNGIZ63QaNXad6dDHUIHmVFzCTLKEXv9CVi75P1yUKinyWhuOJgj2lvQvBo603vl2nD2tg9bh2_WftlOH7TEhs_4H-R_O_oS8me4Fh</recordid><startdate>20141001</startdate><enddate>20141001</enddate><creator>Zadorin, A. I.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20141001</creationdate><title>Modification of the Euler quadrature formula for functions with a boundary-layer component</title><author>Zadorin, A. I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-8728ab1ac452be32e031e8f121a421dc4fdd872ec6ef0650e959fd9d201e11bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Boundaries</topic><topic>Computational mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Construction</topic><topic>Derivatives</topic><topic>Error analysis</topic><topic>Eulers equations</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Quadratures</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zadorin, A. I.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Computational mathematics and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zadorin, A. I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modification of the Euler quadrature formula for functions with a boundary-layer component</atitle><jtitle>Computational mathematics and mathematical physics</jtitle><stitle>Comput. Math. and Math. Phys</stitle><date>2014-10-01</date><risdate>2014</risdate><volume>54</volume><issue>10</issue><spage>1489</spage><epage>1498</epage><pages>1489-1498</pages><issn>0965-5425</issn><eissn>1555-6662</eissn><abstract>The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0965542514100078</doi><tpages>10</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0965-5425
ispartof Computational mathematics and mathematical physics, 2014-10, Vol.54 (10), p.1489-1498
issn 0965-5425
1555-6662
language eng
recordid cdi_proquest_miscellaneous_1629341760
source ABI/INFORM Global; Springer Nature
subjects Boundaries
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Derivatives
Error analysis
Eulers equations
Interpolation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Polynomials
Quadratures
Studies
title Modification of the Euler quadrature formula for functions with a boundary-layer component
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T20%3A10%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Modification%20of%20the%20Euler%20quadrature%20formula%20for%20functions%20with%20a%20boundary-layer%20component&rft.jtitle=Computational%20mathematics%20and%20mathematical%20physics&rft.au=Zadorin,%20A.%20I.&rft.date=2014-10-01&rft.volume=54&rft.issue=10&rft.spage=1489&rft.epage=1498&rft.pages=1489-1498&rft.issn=0965-5425&rft.eissn=1555-6662&rft_id=info:doi/10.1134/S0965542514100078&rft_dat=%3Cproquest_cross%3E3466463661%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c301t-8728ab1ac452be32e031e8f121a421dc4fdd872ec6ef0650e959fd9d201e11bd3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1614370782&rft_id=info:pmid/&rfr_iscdi=true