Meshless method with ridge basis functions for time fractional two-flow domain model
In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the L 1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative ( 0 < α < 1 ) , and b...
Gespeichert in:
| Veröffentlicht in: | Mathematical Sciences 2020-12, Vol.14 (4), p.375-385 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 385 |
|---|---|
| container_issue | 4 |
| container_start_page | 375 |
| container_title | Mathematical Sciences |
| container_volume | 14 |
| creator | Qin, Xinqiang Li, Keyuan Hu, Gang |
| description | In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the
L
1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative
(
0
<
α
<
1
)
, and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple. |
| doi_str_mv | 10.1007/s40096-020-00348-3 |
| format | Article |
| fullrecord | <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_2471560574</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A639207155</galeid><sourcerecordid>A639207155</sourcerecordid><originalsourceid>FETCH-LOGICAL-c239t-d85cda71489d107d01ca1d47fbeea5149c890d5565d8d008b8bc20013aebeb0e3</originalsourceid><addsrcrecordid>eNp9kM1qwzAQhE1poaHNC_Qk6FnpypIs-xhC_yCll_QsZGudKNhWKjmEvn3VuNBbV4ddlvnE7GTZHYMFA1APUQBUBYUcKAAXJeUX2SzPJaNKyOIyzQAlZVxW19k8xj2kUqoCIWfZ5g3jrsMYSY_jzltycuOOBGe3SGoTXSTtcWhG54c0-UBG1yNpgzmvTEfGk6dt50_E-t64gfTeYnebXbWmizj_7TfZx9PjZvVC1-_Pr6vlmjY5r0ZqS9lYo5goK8tAWWCNYVaotkY0komqKSuwUhbSljadUJd1k05h3GCNNSC_ye6nfw_Bfx4xjnrvjyHZijoXiskCpBJJtZhUW9OhdkPrx-Q_PYu9a_yArUv7ZcGrHBIkE5BPQBN8jAFbfQiuN-FLM9A_iespcZ0S1-fENU8Qn6CYxMMWw5-Xf6hvCQGDgA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2471560574</pqid></control><display><type>article</type><title>Meshless method with ridge basis functions for time fractional two-flow domain model</title><source>SpringerLink Journals</source><creator>Qin, Xinqiang ; Li, Keyuan ; Hu, Gang</creator><creatorcontrib>Qin, Xinqiang ; Li, Keyuan ; Hu, Gang</creatorcontrib><description>In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the
L
1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative
(
0
<
α
<
1
)
, and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple.</description><identifier>ISSN: 2008-1359</identifier><identifier>EISSN: 2251-7456</identifier><identifier>DOI: 10.1007/s40096-020-00348-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Approximation ; Basis functions ; Collocation methods ; Comparative analysis ; Domains ; Error analysis ; Finite difference method ; Finite element method ; Flow (Dynamics) ; Interpolation ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Meshless methods ; Methods ; Original Research</subject><ispartof>Mathematical Sciences, 2020-12, Vol.14 (4), p.375-385</ispartof><rights>Islamic Azad University 2020</rights><rights>COPYRIGHT 2020 Springer</rights><rights>Islamic Azad University 2020.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c239t-d85cda71489d107d01ca1d47fbeea5149c890d5565d8d008b8bc20013aebeb0e3</cites><orcidid>0000-0001-5754-2271</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/s40096-020-00348-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40096-020-00348-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Qin, Xinqiang</creatorcontrib><creatorcontrib>Li, Keyuan</creatorcontrib><creatorcontrib>Hu, Gang</creatorcontrib><title>Meshless method with ridge basis functions for time fractional two-flow domain model</title><title>Mathematical Sciences</title><addtitle>Math Sci</addtitle><description>In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the
L
1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative
(
0
<
α
<
1
)
, and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple.</description><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Basis functions</subject><subject>Collocation methods</subject><subject>Comparative analysis</subject><subject>Domains</subject><subject>Error analysis</subject><subject>Finite difference method</subject><subject>Finite element method</subject><subject>Flow (Dynamics)</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Meshless methods</subject><subject>Methods</subject><subject>Original Research</subject><issn>2008-1359</issn><issn>2251-7456</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kM1qwzAQhE1poaHNC_Qk6FnpypIs-xhC_yCll_QsZGudKNhWKjmEvn3VuNBbV4ddlvnE7GTZHYMFA1APUQBUBYUcKAAXJeUX2SzPJaNKyOIyzQAlZVxW19k8xj2kUqoCIWfZ5g3jrsMYSY_jzltycuOOBGe3SGoTXSTtcWhG54c0-UBG1yNpgzmvTEfGk6dt50_E-t64gfTeYnebXbWmizj_7TfZx9PjZvVC1-_Pr6vlmjY5r0ZqS9lYo5goK8tAWWCNYVaotkY0komqKSuwUhbSljadUJd1k05h3GCNNSC_ye6nfw_Bfx4xjnrvjyHZijoXiskCpBJJtZhUW9OhdkPrx-Q_PYu9a_yArUv7ZcGrHBIkE5BPQBN8jAFbfQiuN-FLM9A_iespcZ0S1-fENU8Qn6CYxMMWw5-Xf6hvCQGDgA</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Qin, Xinqiang</creator><creator>Li, Keyuan</creator><creator>Hu, Gang</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0001-5754-2271</orcidid></search><sort><creationdate>20201201</creationdate><title>Meshless method with ridge basis functions for time fractional two-flow domain model</title><author>Qin, Xinqiang ; Li, Keyuan ; Hu, Gang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c239t-d85cda71489d107d01ca1d47fbeea5149c890d5565d8d008b8bc20013aebeb0e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Basis functions</topic><topic>Collocation methods</topic><topic>Comparative analysis</topic><topic>Domains</topic><topic>Error analysis</topic><topic>Finite difference method</topic><topic>Finite element method</topic><topic>Flow (Dynamics)</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Meshless methods</topic><topic>Methods</topic><topic>Original Research</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qin, Xinqiang</creatorcontrib><creatorcontrib>Li, Keyuan</creatorcontrib><creatorcontrib>Hu, Gang</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</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><jtitle>Mathematical Sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qin, Xinqiang</au><au>Li, Keyuan</au><au>Hu, Gang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Meshless method with ridge basis functions for time fractional two-flow domain model</atitle><jtitle>Mathematical Sciences</jtitle><stitle>Math Sci</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>14</volume><issue>4</issue><spage>375</spage><epage>385</epage><pages>375-385</pages><issn>2008-1359</issn><eissn>2251-7456</eissn><abstract>In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the
L
1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative
(
0
<
α
<
1
)
, and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40096-020-00348-3</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0001-5754-2271</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2008-1359 |
| ispartof | Mathematical Sciences, 2020-12, Vol.14 (4), p.375-385 |
| issn | 2008-1359 2251-7456 |
| language | eng |
| recordid | cdi_proquest_journals_2471560574 |
| source | SpringerLink Journals |
| subjects | Applications of Mathematics Approximation Basis functions Collocation methods Comparative analysis Domains Error analysis Finite difference method Finite element method Flow (Dynamics) Interpolation Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Meshless methods Methods Original Research |
| title | Meshless method with ridge basis functions for time fractional two-flow domain model |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-13T10%3A59%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Meshless%20method%20with%20ridge%20basis%20functions%20for%20time%20fractional%20two-flow%20domain%20model&rft.jtitle=Mathematical%20Sciences&rft.au=Qin,%20Xinqiang&rft.date=2020-12-01&rft.volume=14&rft.issue=4&rft.spage=375&rft.epage=385&rft.pages=375-385&rft.issn=2008-1359&rft.eissn=2251-7456&rft_id=info:doi/10.1007/s40096-020-00348-3&rft_dat=%3Cgale_proqu%3EA639207155%3C/gale_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2471560574&rft_id=info:pmid/&rft_galeid=A639207155&rfr_iscdi=true |