Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations
In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order α ∈ ( 0 , 1 ) . The accuracy of these two methods is shown to be of order ( 3 - α ) which improves some previous work done to date. To demonstrate the accuracy and usef...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2023-12, Vol.69 (6), p.4689-4716 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Li, Xuhao Wong, Patricia J. Y. |
| description | In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order
α
∈
(
0
,
1
)
.
The accuracy of these two methods is shown to be of order
(
3
-
α
)
which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations. |
| doi_str_mv | 10.1007/s12190-023-01944-x |
| format | Article |
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α
∈
(
0
,
1
)
.
The accuracy of these two methods is shown to be of order
(
3
-
α
)
which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-023-01944-x</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Approximation ; Computational Mathematics and Numerical Analysis ; Diffusion effects ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Original Research ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2023-12, Vol.69 (6), p.4689-4716</ispartof><rights>The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-82a2c4635af3162bbc293d1eddb7a72c8bc7179d9efb638e13900f6860d1e0293</cites><orcidid>0000-0001-8375-5553</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/s12190-023-01944-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-023-01944-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Li, Xuhao</creatorcontrib><creatorcontrib>Wong, Patricia J. Y.</creatorcontrib><title>Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order
α
∈
(
0
,
1
)
.
The accuracy of these two methods is shown to be of order
(
3
-
α
)
which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations.</description><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Diffusion effects</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Original Research</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOAyEUhonRxFp9AVckrtEDc4OlabwlTdzUNWEYqDTjTAszbfU1fGGZjom6ccUJ-f7vwI_QJYVrClDcBMqoAAIsIUBFmpL9EZpQnmeEAc-O45wJTrJ4cYrOQlgB5IUAMUGfi12LG7PDar327d69qc61TcC29XhpGuNV7T5MhWdq3Xcttl7pAVA1rox320hvDVZNhbtX4_xgqZ0-OLBrcGjrrWuWf0y_FKEvSeWs7cPAm00_Lj9HJ1bVwVx8n1P0cn-3mD2S-fPD0-x2TjQroCOcKabTPMmUTWjOylIzkVTUVFVZqIJpXuqCFqISxpZ5wg1NBIDNeQ4RgshO0dXojT_f9CZ0ctX2Pj4sSCYgzSFLBY8UGynt2xC8sXLtY03-XVKQQ_lyLF_G8uWhfLmPoWQMhQg3S-N_1P-kvgDEvYyi</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Li, Xuhao</creator><creator>Wong, Patricia J. Y.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-8375-5553</orcidid></search><sort><creationdate>20231201</creationdate><title>Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations</title><author>Li, Xuhao ; Wong, Patricia J. Y.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-82a2c4635af3162bbc293d1eddb7a72c8bc7179d9efb638e13900f6860d1e0293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Diffusion effects</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Original Research</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Xuhao</creatorcontrib><creatorcontrib>Wong, Patricia J. Y.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Xuhao</au><au>Wong, Patricia J. Y.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>69</volume><issue>6</issue><spage>4689</spage><epage>4716</epage><pages>4689-4716</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>In this paper, we propose two new approximation methods on a general mesh for the generalized Caputo fractional derivative of order
α
∈
(
0
,
1
)
.
The accuracy of these two methods is shown to be of order
(
3
-
α
)
which improves some previous work done to date. To demonstrate the accuracy and usefulness of the proposed approximations, we carry out experiment on test examples and apply these approximations to solve generalized fractional sub-diffusion equations. The numerical results indicate that the proposed methods perform well in practice. Our contributions lie in two aspects: (i) we propose high order approximations that work on a general mesh; (ii) we establish the well-posedness of generalized fractional sub-diffusion equations and develop numerical schemes using the new high order approximations.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s12190-023-01944-x</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0001-8375-5553</orcidid></addata></record> |
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| ispartof | Journal of applied mathematics & computing, 2023-12, Vol.69 (6), p.4689-4716 |
| issn | 1598-5865 1865-2085 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Approximation Computational Mathematics and Numerical Analysis Diffusion effects Mathematical analysis Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Original Research Theory of Computation |
| title | Two new approximations for generalized Caputo fractional derivative and their application in solving generalized fractional sub-diffusion equations |
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