Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions
It is shown that the Krylov-Bogoliubov methods that give the approximate oscillatory solution of the equation in terms of Jacobi elliptic functions are applicable not only when c 1 >0 and c 3 >0, but also when c 1 >0 and c 3
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| Veröffentlicht in: | International journal of control 1989-04, Vol.49 (4), p.1127-1141 |
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| container_title | International journal of control |
| container_volume | 49 |
| creator | Bravo Yuste, S. Díaz Bejarano, J. |
| description | It is shown that the Krylov-Bogoliubov methods that give the approximate oscillatory solution of the equation
in terms of Jacobi elliptic functions are applicable not only when c
1
>0 and c
3
>0, but also when c
1
>0 and c
3 |
| doi_str_mv | 10.1080/00207178908559696 |
| format | Article |
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in terms of Jacobi elliptic functions are applicable not only when c
1
>0 and c
3
>0, but also when c
1
>0 and c
3
<0 or when c
1
<0 and c
3
>0. In particular, the most precise of these methods, the Christopher-Brocklehurst method, is discussed in detail. Its accuracy has been improved by utilizing the transformation properties of elliptic functions with respect to their parameters.</description><identifier>ISSN: 0020-7179</identifier><identifier>EISSN: 1366-5820</identifier><identifier>DOI: 10.1080/00207178908559696</identifier><identifier>CODEN: IJCOAZ</identifier><language>eng</language><publisher>London: Taylor & Francis Group</publisher><subject>Exact sciences and technology ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Ordinary differential equations ; Sciences and techniques of general use</subject><ispartof>International journal of control, 1989-04, Vol.49 (4), p.1127-1141</ispartof><rights>Copyright Taylor & Francis Group, LLC 1989</rights><rights>1989 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c337t-c2fa148137646adce89cff952a7360be5f499837ac6108b375ed6cfd7f48ee883</citedby><cites>FETCH-LOGICAL-c337t-c2fa148137646adce89cff952a7360be5f499837ac6108b375ed6cfd7f48ee883</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/00207178908559696$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/00207178908559696$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,59646,60435</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7275209$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Bravo Yuste, S.</creatorcontrib><creatorcontrib>Díaz Bejarano, J.</creatorcontrib><title>Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions</title><title>International journal of control</title><description>It is shown that the Krylov-Bogoliubov methods that give the approximate oscillatory solution of the equation
in terms of Jacobi elliptic functions are applicable not only when c
1
>0 and c
3
>0, but also when c
1
>0 and c
3
<0 or when c
1
<0 and c
3
>0. In particular, the most precise of these methods, the Christopher-Brocklehurst method, is discussed in detail. Its accuracy has been improved by utilizing the transformation properties of elliptic functions with respect to their parameters.</description><subject>Exact sciences and technology</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Ordinary differential equations</subject><subject>Sciences and techniques of general use</subject><issn>0020-7179</issn><issn>1366-5820</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNp1kDtPAzEQhC0EEuHxA-hcILoD-xy_JBpAvEQkCqA-OT47Mbqzg-0L5N_jKIEGUW2x38zODgAnGJ1jJNAFQjXimAuJBKWSSbYDRpgwVlFRo10wWu-rAsh9cJDSO0KYUIFH4OX2KxufXPBQ-Ra6fhHD0vTGZ5gDzHMDn-KqC8vqOsxC54ZpWMLe5HloExyS8zNous4tstPQDl7nYpSOwJ5VXTLH23kI3u5uX28eqsnz_ePN1aTShPBc6doqPBaYcDZmqtVGSG2tpLXihKGpoXYspSBcaVZenBJOTcu0bbkdC2OEIIfgbONbMn8MJuWmd0mXPMqbMKSmppRjyUgB8QbUMaQUjW0W0fUqrhqMmnV9zZ_6iuZ0a66SVp2NymuXfoW85rRGsmCXG8x5G2KvPkPs2iar0ln80ZD_r3wDD-2DbQ</recordid><startdate>198904</startdate><enddate>198904</enddate><creator>Bravo Yuste, S.</creator><creator>Díaz Bejarano, J.</creator><general>Taylor & Francis Group</general><general>Taylor & Francis</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>198904</creationdate><title>Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions</title><author>Bravo Yuste, S. ; Díaz Bejarano, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c337t-c2fa148137646adce89cff952a7360be5f499837ac6108b375ed6cfd7f48ee883</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>Exact sciences and technology</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Ordinary differential equations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bravo Yuste, S.</creatorcontrib><creatorcontrib>Díaz Bejarano, J.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science 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><jtitle>International journal of control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bravo Yuste, S.</au><au>Díaz Bejarano, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions</atitle><jtitle>International journal of control</jtitle><date>1989-04</date><risdate>1989</risdate><volume>49</volume><issue>4</issue><spage>1127</spage><epage>1141</epage><pages>1127-1141</pages><issn>0020-7179</issn><eissn>1366-5820</eissn><coden>IJCOAZ</coden><abstract>It is shown that the Krylov-Bogoliubov methods that give the approximate oscillatory solution of the equation
in terms of Jacobi elliptic functions are applicable not only when c
1
>0 and c
3
>0, but also when c
1
>0 and c
3
<0 or when c
1
<0 and c
3
>0. In particular, the most precise of these methods, the Christopher-Brocklehurst method, is discussed in detail. Its accuracy has been improved by utilizing the transformation properties of elliptic functions with respect to their parameters.</abstract><cop>London</cop><pub>Taylor & Francis Group</pub><doi>10.1080/00207178908559696</doi><tpages>15</tpages></addata></record> |
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| ispartof | International journal of control, 1989-04, Vol.49 (4), p.1127-1141 |
| issn | 0020-7179 1366-5820 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_7275209 |
| source | Taylor & Francis:Master (3349 titles) |
| subjects | Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use |
| title | Extension and improvement to the Krylov-Bogoliubov methods using elliptic functions |
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