On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals

This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the or...

Full description

Saved in:
Bibliographic Details
Published in:Numerical analysis and applications 2022-09, Vol.15 (3), p.203-218
Main Authors: Boikov, I. V, Boikova, A. I
Format: Article
Language:English
Subjects:
Convergence
Errors
Integrals
Mathematics
Mathematics and Statistics
Numerical Analysis
Quadratures
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-c268t-10ecc38ea768cb0b892b201feeae9efd34af5da9feada9ca48fdcdc100a8b5a63
container_end_page 218
container_issue 3
container_start_page 203
container_title Numerical analysis and applications
container_volume 15
creator Boikov, I. V
Boikova, A. I
description This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the original integral for   with weights ,  . In the latter case, a sequence of quadrature formulas converges to the integral uniformly on [ ], where   is arbitrarily small. We propose a method for constructing and estimating the errors of quadrature formulas to evaluate hypersingular integrals by transforming quadrature formulas to evaluate singular integrals. We also propose a method for estimating the errors of quadrature formulas for singular integral evaluation based on approximation theory methods. The results obtained have been extended to hypersingular integrals.
doi_str_mv 10.1134/S199542392203003X
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2707227460</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2707227460</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-10ecc38ea768cb0b892b201feeae9efd34af5da9feada9ca48fdcdc100a8b5a63</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWGp_gLeA59V8dTc5SrG2UCmiBW9LNjupLe1mnewe-u9NrehBnMPMMPO878AQcs3ZLedS3b1wY8ZKSCMEk4zJtzMyOI4yJVRx_tNLc0lGMW5ZCikKrfIBWS0baukTdO-hpsHTSWhih73rNs2aPve2Rtv1CHQacN_vbKQ-YIL2bf9FzA4tYExd2iGdNx2s0e7iFbnwqcDouw7JavrwOplli-XjfHK_yJzIdZdxBs5JDbbItatYpY2oBOMewIIBX0tl_bi2xoNN2Vmlfe1qxxmzuhrbXA7Jzcm3xfDRQ-zKbeixSSdLUbBCiELlLFH8RDkMMSL4ssXN3uKh5Kw8PrD888CkESdNTGyzBvx1_l_0CTeHdHI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2707227460</pqid></control><display><type>article</type><title>On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals</title><source>Springer Nature</source><creator>Boikov, I. V ; Boikova, A. I</creator><creatorcontrib>Boikov, I. V ; Boikova, A. I</creatorcontrib><description>This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the original integral for   with weights ,  . In the latter case, a sequence of quadrature formulas converges to the integral uniformly on [ ], where   is arbitrarily small. We propose a method for constructing and estimating the errors of quadrature formulas to evaluate hypersingular integrals by transforming quadrature formulas to evaluate singular integrals. We also propose a method for estimating the errors of quadrature formulas for singular integral evaluation based on approximation theory methods. The results obtained have been extended to hypersingular integrals.</description><identifier>ISSN: 1995-4239</identifier><identifier>EISSN: 1995-4247</identifier><identifier>DOI: 10.1134/S199542392203003X</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Convergence ; Errors ; Integrals ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Quadratures</subject><ispartof>Numerical analysis and applications, 2022-09, Vol.15 (3), p.203-218</ispartof><rights>Pleiades Publishing, Ltd. 2022</rights><rights>Pleiades Publishing, Ltd. 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-10ecc38ea768cb0b892b201feeae9efd34af5da9feada9ca48fdcdc100a8b5a63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Boikov, I. V</creatorcontrib><creatorcontrib>Boikova, A. I</creatorcontrib><title>On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals</title><title>Numerical analysis and applications</title><addtitle>Numer. Analys. Appl</addtitle><description>This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the original integral for   with weights ,  . In the latter case, a sequence of quadrature formulas converges to the integral uniformly on [ ], where   is arbitrarily small. We propose a method for constructing and estimating the errors of quadrature formulas to evaluate hypersingular integrals by transforming quadrature formulas to evaluate singular integrals. We also propose a method for estimating the errors of quadrature formulas for singular integral evaluation based on approximation theory methods. The results obtained have been extended to hypersingular integrals.</description><subject>Convergence</subject><subject>Errors</subject><subject>Integrals</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Quadratures</subject><issn>1995-4239</issn><issn>1995-4247</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWGp_gLeA59V8dTc5SrG2UCmiBW9LNjupLe1mnewe-u9NrehBnMPMMPO878AQcs3ZLedS3b1wY8ZKSCMEk4zJtzMyOI4yJVRx_tNLc0lGMW5ZCikKrfIBWS0baukTdO-hpsHTSWhih73rNs2aPve2Rtv1CHQacN_vbKQ-YIL2bf9FzA4tYExd2iGdNx2s0e7iFbnwqcDouw7JavrwOplli-XjfHK_yJzIdZdxBs5JDbbItatYpY2oBOMewIIBX0tl_bi2xoNN2Vmlfe1qxxmzuhrbXA7Jzcm3xfDRQ-zKbeixSSdLUbBCiELlLFH8RDkMMSL4ssXN3uKh5Kw8PrD888CkESdNTGyzBvx1_l_0CTeHdHI</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Boikov, I. V</creator><creator>Boikova, A. I</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220901</creationdate><title>On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals</title><author>Boikov, I. V ; Boikova, A. I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-10ecc38ea768cb0b892b201feeae9efd34af5da9feada9ca48fdcdc100a8b5a63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Convergence</topic><topic>Errors</topic><topic>Integrals</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Quadratures</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Boikov, I. V</creatorcontrib><creatorcontrib>Boikova, A. I</creatorcontrib><collection>CrossRef</collection><jtitle>Numerical analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Boikov, I. V</au><au>Boikova, A. I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals</atitle><jtitle>Numerical analysis and applications</jtitle><stitle>Numer. Analys. Appl</stitle><date>2022-09-01</date><risdate>2022</risdate><volume>15</volume><issue>3</issue><spage>203</spage><epage>218</epage><pages>203-218</pages><issn>1995-4239</issn><eissn>1995-4247</eissn><abstract>This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the original integral for   with weights ,  . In the latter case, a sequence of quadrature formulas converges to the integral uniformly on [ ], where   is arbitrarily small. We propose a method for constructing and estimating the errors of quadrature formulas to evaluate hypersingular integrals by transforming quadrature formulas to evaluate singular integrals. We also propose a method for estimating the errors of quadrature formulas for singular integral evaluation based on approximation theory methods. The results obtained have been extended to hypersingular integrals.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S199542392203003X</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1995-4239
ispartof Numerical analysis and applications, 2022-09, Vol.15 (3), p.203-218
issn 1995-4239
1995-4247
language eng
recordid cdi_proquest_journals_2707227460
source Springer Nature
subjects Convergence
Errors
Integrals
Mathematics
Mathematics and Statistics
Numerical Analysis
Quadratures
title On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T15%3A39%3A11IST&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=On%20a%20Method%20of%20Constructing%20Quadrature%20Formulas%20for%20Computing%20Hypersingular%20Integrals&rft.jtitle=Numerical%20analysis%20and%20applications&rft.au=Boikov,%20I.%20V&rft.date=2022-09-01&rft.volume=15&rft.issue=3&rft.spage=203&rft.epage=218&rft.pages=203-218&rft.issn=1995-4239&rft.eissn=1995-4247&rft_id=info:doi/10.1134/S199542392203003X&rft_dat=%3Cproquest_cross%3E2707227460%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c268t-10ecc38ea768cb0b892b201feeae9efd34af5da9feada9ca48fdcdc100a8b5a63%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2707227460&rft_id=info:pmid/&rfr_iscdi=true