Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation
The main purpose of this paper is to design a numerical method for solving the space–time fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order O ( τ 2 - β ) . In the next, to discrete the sp...
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| Veröffentlicht in: | Engineering with computers 2022-04, Vol.38 (2), p.1409-1420 |
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| creator | Safdari, H. Aghdam, Y. Esmaeelzade Gómez-Aguilar, J. F. |
| description | The main purpose of this paper is to design a numerical method for solving the space–time fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order
O
(
τ
2
-
β
)
. In the next, to discrete the spatial fractional derivative, the Chebyshev collocation method of the fourth kind has been applied. This discrete scheme is based on the closed formula for the spatial fractional derivative. Besides, the time-discrete scheme has studied in the
L
2
space by the energy method and we have proved the unconditional stability and convergence order. Finally, we solve three examples by the proposed method and the obtained results are compared with other numerical problems. The numerical results show that our method is much more accurate than existing techniques in the literature. |
| doi_str_mv | 10.1007/s00366-020-01092-x |
| format | Article |
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O
(
τ
2
-
β
)
. In the next, to discrete the spatial fractional derivative, the Chebyshev collocation method of the fourth kind has been applied. This discrete scheme is based on the closed formula for the spatial fractional derivative. Besides, the time-discrete scheme has studied in the
L
2
space by the energy method and we have proved the unconditional stability and convergence order. Finally, we solve three examples by the proposed method and the obtained results are compared with other numerical problems. The numerical results show that our method is much more accurate than existing techniques in the literature.</description><identifier>ISSN: 0177-0667</identifier><identifier>EISSN: 1435-5663</identifier><identifier>DOI: 10.1007/s00366-020-01092-x</identifier><language>eng</language><publisher>London: Springer London</publisher><subject>Advection ; Advection-diffusion equation ; Boundary conditions ; CAE) and Design ; Calculus of Variations and Optimal Control; Optimization ; Chebyshev approximation ; Classical Mechanics ; Collocation methods ; Computer Science ; Computer-Aided Engineering (CAD ; Control ; Convergence ; Energy methods ; Finite difference method ; Laplace transforms ; Math. Applications in Chemistry ; Mathematical and Computational Engineering ; Numerical methods ; Original Article ; Partial differential equations ; Systems Theory</subject><ispartof>Engineering with computers, 2022-04, Vol.38 (2), p.1409-1420</ispartof><rights>Springer-Verlag London Ltd., part of Springer Nature 2020</rights><rights>Springer-Verlag London Ltd., part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-3f66a8be57266660582eab55f9e21829c0d7930f52e504363e01e815f9b03a063</citedby><cites>FETCH-LOGICAL-c319t-3f66a8be57266660582eab55f9e21829c0d7930f52e504363e01e815f9b03a063</cites><orcidid>0000-0002-4050-7450 ; 0000-0001-5109-1561 ; 0000-0001-9403-3767</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/s00366-020-01092-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00366-020-01092-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Safdari, H.</creatorcontrib><creatorcontrib>Aghdam, Y. Esmaeelzade</creatorcontrib><creatorcontrib>Gómez-Aguilar, J. F.</creatorcontrib><title>Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation</title><title>Engineering with computers</title><addtitle>Engineering with Computers</addtitle><description>The main purpose of this paper is to design a numerical method for solving the space–time fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order
O
(
τ
2
-
β
)
. In the next, to discrete the spatial fractional derivative, the Chebyshev collocation method of the fourth kind has been applied. This discrete scheme is based on the closed formula for the spatial fractional derivative. Besides, the time-discrete scheme has studied in the
L
2
space by the energy method and we have proved the unconditional stability and convergence order. Finally, we solve three examples by the proposed method and the obtained results are compared with other numerical problems. The numerical results show that our method is much more accurate than existing techniques in the literature.</description><subject>Advection</subject><subject>Advection-diffusion equation</subject><subject>Boundary conditions</subject><subject>CAE) and Design</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Chebyshev approximation</subject><subject>Classical Mechanics</subject><subject>Collocation methods</subject><subject>Computer Science</subject><subject>Computer-Aided Engineering (CAD</subject><subject>Control</subject><subject>Convergence</subject><subject>Energy methods</subject><subject>Finite difference method</subject><subject>Laplace transforms</subject><subject>Math. Applications in Chemistry</subject><subject>Mathematical and Computational Engineering</subject><subject>Numerical methods</subject><subject>Original Article</subject><subject>Partial differential equations</subject><subject>Systems Theory</subject><issn>0177-0667</issn><issn>1435-5663</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kD1OAzEQhS0EEiFwASpL1IaxHXuzJYr4kyJRALXleMfZDZvdxN4E0tFxAG7ISXASJDrceKT53puZR8g5h0sOkF1FAKk1AwEMOOSCvR-QHh9IxZTW8pD0gGcZA62zY3IS4wyAS4C8Rz6fysp3WNBRiZNNLHFNXVvXrbNd1Ta09bQrkfp2FbqSvlZNQd-qVLm2WWOYYuOQ2sbWm1jFRIUdHRfW4ffHV1fNkzRYt7WyNbXFGnc1KyrvV3E7AJer3aRTcuRtHfHs9--Tl9ub59E9Gz_ePYyux8xJnndMeq3tcIIqEzo9UEOBdqKUz1HwocgdFFkuwSuBCgZSSwSOQ576E5AWtOyTi73vIrTLFcbOzNJtabtohB5k-SDjakuJPeVCG2NAbxahmtuwMRzMNnCzD9ykwM0ucPOeRHIvigluphj-rP9R_QBcY4cP</recordid><startdate>20220401</startdate><enddate>20220401</enddate><creator>Safdari, H.</creator><creator>Aghdam, Y. 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Esmaeelzade ; Gómez-Aguilar, J. F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-3f66a8be57266660582eab55f9e21829c0d7930f52e504363e01e815f9b03a063</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Advection</topic><topic>Advection-diffusion equation</topic><topic>Boundary conditions</topic><topic>CAE) and Design</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Chebyshev approximation</topic><topic>Classical Mechanics</topic><topic>Collocation methods</topic><topic>Computer Science</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Control</topic><topic>Convergence</topic><topic>Energy methods</topic><topic>Finite difference method</topic><topic>Laplace transforms</topic><topic>Math. Applications in Chemistry</topic><topic>Mathematical and Computational Engineering</topic><topic>Numerical methods</topic><topic>Original Article</topic><topic>Partial differential equations</topic><topic>Systems Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Safdari, H.</creatorcontrib><creatorcontrib>Aghdam, Y. Esmaeelzade</creatorcontrib><creatorcontrib>Gómez-Aguilar, J. 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Esmaeelzade</au><au>Gómez-Aguilar, J. F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation</atitle><jtitle>Engineering with computers</jtitle><stitle>Engineering with Computers</stitle><date>2022-04-01</date><risdate>2022</risdate><volume>38</volume><issue>2</issue><spage>1409</spage><epage>1420</epage><pages>1409-1420</pages><issn>0177-0667</issn><eissn>1435-5663</eissn><abstract>The main purpose of this paper is to design a numerical method for solving the space–time fractional advection-diffusion equation (STFADE). First, a finite difference scheme is applied to obtain the semi-discrete in time variable with convergence order
O
(
τ
2
-
β
)
. In the next, to discrete the spatial fractional derivative, the Chebyshev collocation method of the fourth kind has been applied. This discrete scheme is based on the closed formula for the spatial fractional derivative. Besides, the time-discrete scheme has studied in the
L
2
space by the energy method and we have proved the unconditional stability and convergence order. Finally, we solve three examples by the proposed method and the obtained results are compared with other numerical problems. The numerical results show that our method is much more accurate than existing techniques in the literature.</abstract><cop>London</cop><pub>Springer London</pub><doi>10.1007/s00366-020-01092-x</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-4050-7450</orcidid><orcidid>https://orcid.org/0000-0001-5109-1561</orcidid><orcidid>https://orcid.org/0000-0001-9403-3767</orcidid></addata></record> |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Advection Advection-diffusion equation Boundary conditions CAE) and Design Calculus of Variations and Optimal Control Optimization Chebyshev approximation Classical Mechanics Collocation methods Computer Science Computer-Aided Engineering (CAD Control Convergence Energy methods Finite difference method Laplace transforms Math. Applications in Chemistry Mathematical and Computational Engineering Numerical methods Original Article Partial differential equations Systems Theory |
| title | Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space–time fractional advection-diffusion equation |
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