Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations
In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm i...
Gespeichert in:
| Veröffentlicht in: | Advances in difference equations 2015-07, Vol.2015 (1), p.1-15, Article 237 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 15 |
|---|---|
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Advances in difference equations |
| container_volume | 2015 |
| creator | Zhang, Xiao-yong Wan, Zheng-su |
| description | In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of this new approach and coincide well with theoretical analysis. |
| doi_str_mv | 10.1186/s13662-015-0562-z |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1800496242</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1800496242</sourcerecordid><originalsourceid>FETCH-LOGICAL-c344t-fda10d262a500a9d2c1801f11b501dc4ff457db15672027454d1d49cf76787e93</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhhdRsFZ_gLcFL15WM9lssnuU4icFL3oO6SZpU7ZJm2TV9tebuh6K4Glm4HlfmCfLLgHdANT0NkBJKS4QVAWq0rI7ykZAa1ZATdjxwX6anYWwRAg3pK5HWfciWjczufNx4ebOii4X67V3X2YlonE2_zRxkVs1T9eHyo2Naq58LqzMTQx7tjPtQEaXWqSxwm9zabRWXtloUqHa9D9EOM9OtOiCuvid4-z94f5t8lRMXx-fJ3fToi0JiYWWApDEFIsKIdFI3EKNQAPMKgSyJVqTiskZVJRhhBmpiARJmlYzymqmmnKcXQ-96ZFNr0LkKxNa1XXCKtcHnuoQaSgmOKFXf9Cl633SkCiGEKIlZVWiYKBa70LwSvO1T4L8lgPie_988M-Tf773z3cpg4dMSKxN0g6a_w19A5lKijk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1700063675</pqid></control><display><type>article</type><title>Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations</title><source>DOAJ Directory of Open Access Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Zhang, Xiao-yong ; Wan, Zheng-su</creator><creatorcontrib>Zhang, Xiao-yong ; Wan, Zheng-su</creatorcontrib><description>In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of this new approach and coincide well with theoretical analysis.</description><identifier>ISSN: 1687-1847</identifier><identifier>ISSN: 1687-1839</identifier><identifier>EISSN: 1687-1847</identifier><identifier>DOI: 10.1186/s13662-015-0562-z</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximation ; Convergence ; Difference and Functional Equations ; Differential equations ; Functional Analysis ; Integers ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Spectra ; Spectral methods</subject><ispartof>Advances in difference equations, 2015-07, Vol.2015 (1), p.1-15, Article 237</ispartof><rights>Zhang and Wan 2015</rights><rights>The Author(s) 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c344t-fda10d262a500a9d2c1801f11b501dc4ff457db15672027454d1d49cf76787e93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,860,27901,27902</link.rule.ids></links><search><creatorcontrib>Zhang, Xiao-yong</creatorcontrib><creatorcontrib>Wan, Zheng-su</creatorcontrib><title>Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations</title><title>Advances in difference equations</title><addtitle>Adv Differ Equ</addtitle><description>In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of this new approach and coincide well with theoretical analysis.</description><subject>Analysis</subject><subject>Approximation</subject><subject>Convergence</subject><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Functional Analysis</subject><subject>Integers</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Spectra</subject><subject>Spectral methods</subject><issn>1687-1847</issn><issn>1687-1839</issn><issn>1687-1847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNp1kE1LAzEQhhdRsFZ_gLcFL15WM9lssnuU4icFL3oO6SZpU7ZJm2TV9tebuh6K4Glm4HlfmCfLLgHdANT0NkBJKS4QVAWq0rI7ykZAa1ZATdjxwX6anYWwRAg3pK5HWfciWjczufNx4ebOii4X67V3X2YlonE2_zRxkVs1T9eHyo2Naq58LqzMTQx7tjPtQEaXWqSxwm9zabRWXtloUqHa9D9EOM9OtOiCuvid4-z94f5t8lRMXx-fJ3fToi0JiYWWApDEFIsKIdFI3EKNQAPMKgSyJVqTiskZVJRhhBmpiARJmlYzymqmmnKcXQ-96ZFNr0LkKxNa1XXCKtcHnuoQaSgmOKFXf9Cl633SkCiGEKIlZVWiYKBa70LwSvO1T4L8lgPie_988M-Tf773z3cpg4dMSKxN0g6a_w19A5lKijk</recordid><startdate>20150730</startdate><enddate>20150730</enddate><creator>Zhang, Xiao-yong</creator><creator>Wan, Zheng-su</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20150730</creationdate><title>Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations</title><author>Zhang, Xiao-yong ; Wan, Zheng-su</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c344t-fda10d262a500a9d2c1801f11b501dc4ff457db15672027454d1d49cf76787e93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Approximation</topic><topic>Convergence</topic><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Functional Analysis</topic><topic>Integers</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Spectra</topic><topic>Spectral methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Xiao-yong</creatorcontrib><creatorcontrib>Wan, Zheng-su</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</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>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</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>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</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>ProQuest Central Basic</collection><jtitle>Advances in difference equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Xiao-yong</au><au>Wan, Zheng-su</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations</atitle><jtitle>Advances in difference equations</jtitle><stitle>Adv Differ Equ</stitle><date>2015-07-30</date><risdate>2015</risdate><volume>2015</volume><issue>1</issue><spage>1</spage><epage>15</epage><pages>1-15</pages><artnum>237</artnum><issn>1687-1847</issn><issn>1687-1839</issn><eissn>1687-1847</eissn><abstract>In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of this new approach and coincide well with theoretical analysis.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13662-015-0562-z</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1687-1847 |
| ispartof | Advances in difference equations, 2015-07, Vol.2015 (1), p.1-15, Article 237 |
| issn | 1687-1847 1687-1839 1687-1847 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1800496242 |
| source | DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Analysis Approximation Convergence Difference and Functional Equations Differential equations Functional Analysis Integers Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Spectra Spectral methods |
| title | Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-03T07%3A35%3A32IST&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=Jacobi%20orthogonal%20approximation%20with%20negative%20integer%20and%20its%20application%20to%20ordinary%20differential%20equations&rft.jtitle=Advances%20in%20difference%20equations&rft.au=Zhang,%20Xiao-yong&rft.date=2015-07-30&rft.volume=2015&rft.issue=1&rft.spage=1&rft.epage=15&rft.pages=1-15&rft.artnum=237&rft.issn=1687-1847&rft.eissn=1687-1847&rft_id=info:doi/10.1186/s13662-015-0562-z&rft_dat=%3Cproquest_cross%3E1800496242%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1700063675&rft_id=info:pmid/&rfr_iscdi=true |