Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods
For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynom...
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| Veröffentlicht in: | Afrika mathematica 2019-06, Vol.30 (3-4), p.469-482 |
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| container_title | Afrika mathematica |
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| creator | Allouch, C. Sbibih, D. Tahrichi, M. |
| description | For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree
≤
r
-
1
.
We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4
r
in the interpolation at Gauss points can be improved to
4
r
+
2
. We illustrate the improvement of the order of convergence by numerical experiments. |
| doi_str_mv | 10.1007/s13370-019-00660-9 |
| format | Article |
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≤
r
-
1
.
We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4
r
in the interpolation at Gauss points can be improved to
4
r
+
2
. We illustrate the improvement of the order of convergence by numerical experiments.</description><identifier>ISSN: 1012-9405</identifier><identifier>EISSN: 2190-7668</identifier><identifier>DOI: 10.1007/s13370-019-00660-9</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Approximation ; Asymptotic series ; Convergence ; Extrapolation ; History of Mathematical Sciences ; Integral equations ; Interpolation ; Kernels ; Mathematics ; Mathematics and Statistics ; Mathematics Education ; Polynomials</subject><ispartof>Afrika mathematica, 2019-06, Vol.30 (3-4), p.469-482</ispartof><rights>African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-bdf066545e6d15c21074b6945c67740b0433dfbe228e653ef39f3ef952147c503</citedby><cites>FETCH-LOGICAL-c319t-bdf066545e6d15c21074b6945c67740b0433dfbe228e653ef39f3ef952147c503</cites><orcidid>0000-0001-7898-4503</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13370-019-00660-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13370-019-00660-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Allouch, C.</creatorcontrib><creatorcontrib>Sbibih, D.</creatorcontrib><creatorcontrib>Tahrichi, M.</creatorcontrib><title>Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods</title><title>Afrika mathematica</title><addtitle>Afr. Mat</addtitle><description>For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree
≤
r
-
1
.
We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4
r
in the interpolation at Gauss points can be improved to
4
r
+
2
. We illustrate the improvement of the order of convergence by numerical experiments.</description><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Asymptotic series</subject><subject>Convergence</subject><subject>Extrapolation</subject><subject>History of Mathematical Sciences</subject><subject>Integral equations</subject><subject>Interpolation</subject><subject>Kernels</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics Education</subject><subject>Polynomials</subject><issn>1012-9405</issn><issn>2190-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9UMlKBDEQDaLgMM4PeGrwHK2sPTnK4AaiIAreQrpTPYsz3W2SEefH_AF_zGgL3qxDbbxXyyPkmMEpAyjPIhOiBArMUACtgZo9MuLMAC21nu6TEQPGqZGgDskkxhVkk5ppJUbk-WFZL1zwsWsLfE_B9d3apWWuKhfRFzmJ2x5D3bVvGObYpuJuF1P4_NgUrvWFx9zD4BIWLxhaXBcbTIvOxyNy0Lh1xMlvHJOny4vH2TW9vb-6mZ3f0lowk2jlm3yykgq1Z6rmDEpZaSNVrctSQgVSCN9UyPkU88HYCNNkbxRnsqwViDE5Geb2oXvdYkx21W1Dm1dazrnMT4PkGcUHVB26GAM2tg_LjQs7y8B-i2gHEW0W0f6IaE0miYEUM7idY_gb_Q_rC88NdYM</recordid><startdate>20190601</startdate><enddate>20190601</enddate><creator>Allouch, C.</creator><creator>Sbibih, D.</creator><creator>Tahrichi, M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-7898-4503</orcidid></search><sort><creationdate>20190601</creationdate><title>Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods</title><author>Allouch, C. ; Sbibih, D. ; Tahrichi, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-bdf066545e6d15c21074b6945c67740b0433dfbe228e653ef39f3ef952147c503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Asymptotic series</topic><topic>Convergence</topic><topic>Extrapolation</topic><topic>History of Mathematical Sciences</topic><topic>Integral equations</topic><topic>Interpolation</topic><topic>Kernels</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics Education</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Allouch, C.</creatorcontrib><creatorcontrib>Sbibih, D.</creatorcontrib><creatorcontrib>Tahrichi, M.</creatorcontrib><collection>CrossRef</collection><jtitle>Afrika mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Allouch, C.</au><au>Sbibih, D.</au><au>Tahrichi, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods</atitle><jtitle>Afrika mathematica</jtitle><stitle>Afr. Mat</stitle><date>2019-06-01</date><risdate>2019</risdate><volume>30</volume><issue>3-4</issue><spage>469</spage><epage>482</epage><pages>469-482</pages><issn>1012-9405</issn><eissn>2190-7668</eissn><abstract>For computing the approximated solution of a second kind integral equation with a smooth kernel, we investigate in this paper the Richardson extrapolation using superconvergent Nyström and degenerate kernel methods based on interpolatory projection onto the space of (discontinuous) piecewise polynomials of degree
≤
r
-
1
.
We obtain asymptotic series expansions for the approximate solutions and we show that the order of convergence 4
r
in the interpolation at Gauss points can be improved to
4
r
+
2
. We illustrate the improvement of the order of convergence by numerical experiments.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s13370-019-00660-9</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0001-7898-4503</orcidid></addata></record> |
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| ispartof | Afrika mathematica, 2019-06, Vol.30 (3-4), p.469-482 |
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| language | eng |
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| subjects | Applications of Mathematics Approximation Asymptotic series Convergence Extrapolation History of Mathematical Sciences Integral equations Interpolation Kernels Mathematics Mathematics and Statistics Mathematics Education Polynomials |
| title | Richardson extrapolation based on superconvergent Nyström and degenerate kernel methods |
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