An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis
The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) based on a spectral Tau method. An extension of the operational approach of the Tau method with the orthogonal polynomial bases is proposed to convert FDEs to its matrix–vect...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2011, Vol.61 (1), p.30-43 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Ghoreishi, F. Yazdani, S. |
| description | The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) based on a spectral Tau method. An extension of the operational approach of the Tau method with the orthogonal polynomial bases is proposed to convert FDEs to its matrix–vector multiplication representation. The fractional derivatives are described in the Caputo sense. The spectral rate of convergence for the proposed method is established in the
L
2
norm. We tested our procedure on several examples and observed that the obtained numerical results confirm the theoretical prediction of the exponential rate of convergence. |
| doi_str_mv | 10.1016/j.camwa.2010.10.027 |
| format | Article |
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L
2
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L
2
norm. We tested our procedure on several examples and observed that the obtained numerical results confirm the theoretical prediction of the exponential rate of convergence.</description><subject>Caputo derivative</subject><subject>Computer simulation</subject><subject>Convergence</subject><subject>Derivatives</subject><subject>Differential equations</subject><subject>Fractional differential equations</subject><subject>Mathematical models</subject><subject>Multiplication</subject><subject>Norms</subject><subject>Operational approach to the Tau method</subject><subject>Representations</subject><subject>Spectra</subject><subject>Tau method</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwBWy8Y5Vi52VnwaKqeEmV2JS15Thj6iqJW9tp6Sfw1zgta1ajuXPvjOYgdE_JjBJaPm5mSnYHOUvJSZmRlF2gCeUsS1hZ8ks0IbziCU1Teo1uvN8QQvIsJRP0M-8xfAfovbE9thqHNWC_BRWcbPFKDriDsLYN1tbhfujAGRUH3rZD-Et0QxtMYl0DDmsn1ahHS2O0Bgd9MLGB3SBH3eODCWusbL8H9wW9Aiyj-eiNv0VXWrYe7v7qFH2-PK8Wb8ny4_V9MV8mKuMkJJwyVadcM1XJUlcZ0wWjed4wlsV7OuW0ZrykOdG1IqSgZapVTUtWVKTOOZBsih7Oe7fO7gbwQXTGK2hb2YMdvOBFUVZFkbHozM5O5az3DrTYOtNJdxSUiJG72IgTdzFyH8XIPaaezimIT-wNOOGVGT9tjItYRWPNv_lfjVWQBQ</recordid><startdate>2011</startdate><enddate>2011</enddate><creator>Ghoreishi, F.</creator><creator>Yazdani, S.</creator><general>Elsevier Ltd</general><scope>6I.</scope><scope>AAFTH</scope><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></search><sort><creationdate>2011</creationdate><title>An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis</title><author>Ghoreishi, F. ; Yazdani, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-817cb28f7c9a6f937f57144d773ffef281b786140fbc005162fcb167590b48e03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Caputo derivative</topic><topic>Computer simulation</topic><topic>Convergence</topic><topic>Derivatives</topic><topic>Differential equations</topic><topic>Fractional differential equations</topic><topic>Mathematical models</topic><topic>Multiplication</topic><topic>Norms</topic><topic>Operational approach to the Tau method</topic><topic>Representations</topic><topic>Spectra</topic><topic>Tau method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghoreishi, F.</creatorcontrib><creatorcontrib>Yazdani, S.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><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>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ghoreishi, F.</au><au>Yazdani, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2011</date><risdate>2011</risdate><volume>61</volume><issue>1</issue><spage>30</spage><epage>43</epage><pages>30-43</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) based on a spectral Tau method. An extension of the operational approach of the Tau method with the orthogonal polynomial bases is proposed to convert FDEs to its matrix–vector multiplication representation. The fractional derivatives are described in the Caputo sense. The spectral rate of convergence for the proposed method is established in the
L
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| ispartof | Computers & mathematics with applications (1987), 2011, Vol.61 (1), p.30-43 |
| issn | 0898-1221 1873-7668 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_855695537 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Caputo derivative Computer simulation Convergence Derivatives Differential equations Fractional differential equations Mathematical models Multiplication Norms Operational approach to the Tau method Representations Spectra Tau method |
| title | An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis |
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