Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability
In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Ri...
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| Veröffentlicht in: | The Journal of supercomputing 2024, Vol.80 (12), p.16887-16917 |
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| container_title | The Journal of supercomputing |
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| creator | Saedshoar Heris, Mahdi Javidi, Mohammad |
| description | In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of
O
(
h
2
+
k
2
+
κ
2
+
σ
2
+
ρ
2
)
, where
h
,
k
and
κ
are space step for
x
,
y
and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution. |
| doi_str_mv | 10.1007/s11227-024-06112-x |
| format | Article |
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O
(
h
2
+
k
2
+
κ
2
+
σ
2
+
ρ
2
)
, where
h
,
k
and
κ
are space step for
x
,
y
and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution.</description><identifier>ISSN: 0920-8542</identifier><identifier>EISSN: 1573-0484</identifier><identifier>DOI: 10.1007/s11227-024-06112-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Advection ; Advection-diffusion equation ; Compilers ; Computer Science ; Exact solutions ; Finite difference method ; Interpreters ; Mathematical analysis ; Numerical methods ; Operators (mathematics) ; Processor Architectures ; Programming Languages</subject><ispartof>The Journal of supercomputing, 2024, Vol.80 (12), p.16887-16917</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. 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-aab0f2b39bee22f213956f975a215b9cf8ce839286154727e807fb89a7d1e11a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11227-024-06112-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11227-024-06112-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Saedshoar Heris, Mahdi</creatorcontrib><creatorcontrib>Javidi, Mohammad</creatorcontrib><title>Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability</title><title>The Journal of supercomputing</title><addtitle>J Supercomput</addtitle><description>In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of
O
(
h
2
+
k
2
+
κ
2
+
σ
2
+
ρ
2
)
, where
h
,
k
and
κ
are space step for
x
,
y
and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution.</description><subject>Advection</subject><subject>Advection-diffusion equation</subject><subject>Compilers</subject><subject>Computer Science</subject><subject>Exact solutions</subject><subject>Finite difference method</subject><subject>Interpreters</subject><subject>Mathematical analysis</subject><subject>Numerical methods</subject><subject>Operators (mathematics)</subject><subject>Processor Architectures</subject><subject>Programming Languages</subject><issn>0920-8542</issn><issn>1573-0484</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4CrgOprLTDPjTqpVoSCIrkNm5qRNaTNtkqmtK7eufUOfxJlWcOfq_Bz-C3wInTN6ySiVV4ExziWhPCF00GqyOUA9lkpBaJIlh6hHc05Jlib8GJ2EMKOUJkKKHvocWWcj4MoaAx5cCXgBcVpX2NQexyngZwvhHYelLjtXiN4WTYSK1L4Cj3W1hjLa2n1_fHUdTWg1hlWjuyd-s3GKK5jrLbYO89trXNZuDX6yW9KuwiHqws5t3J6iI6PnAc5-bx-9ju5ehg9k_HT_OLwZk5JLGonWBTW8EHkBwLnhTOTpwOQy1ZylRV6arIRM5DwbsDSRXEJGpSmyXMuKAWNa9NHFvnfp61UDIapZ3XjXTipBpWxByba0j_jeVfo6BA9GLb1daL9VjKoOudojVy1ytUOuNm1I7EOhNbsJ-L_qf1I_cvqH4g</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Saedshoar Heris, Mahdi</creator><creator>Javidi, Mohammad</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2024</creationdate><title>Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability</title><author>Saedshoar Heris, Mahdi ; Javidi, Mohammad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-aab0f2b39bee22f213956f975a215b9cf8ce839286154727e807fb89a7d1e11a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Advection</topic><topic>Advection-diffusion equation</topic><topic>Compilers</topic><topic>Computer Science</topic><topic>Exact solutions</topic><topic>Finite difference method</topic><topic>Interpreters</topic><topic>Mathematical analysis</topic><topic>Numerical methods</topic><topic>Operators (mathematics)</topic><topic>Processor Architectures</topic><topic>Programming Languages</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saedshoar Heris, Mahdi</creatorcontrib><creatorcontrib>Javidi, Mohammad</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of supercomputing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saedshoar Heris, Mahdi</au><au>Javidi, Mohammad</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability</atitle><jtitle>The Journal of supercomputing</jtitle><stitle>J Supercomput</stitle><date>2024</date><risdate>2024</risdate><volume>80</volume><issue>12</issue><spage>16887</spage><epage>16917</epage><pages>16887-16917</pages><issn>0920-8542</issn><eissn>1573-0484</eissn><abstract>In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the fractional backward differential formula method of second order (FBDF2), and weighted and shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and develop the finite difference method for the RFADED. It has been shown that the obtained schemes are unconditionally stable and convergent with the accuracy of
O
(
h
2
+
k
2
+
κ
2
+
σ
2
+
ρ
2
)
, where
h
,
k
and
κ
are space step for
x
,
y
and time step, respectively. Also, numerical examples are constructed to demonstrate the effectiveness of the numerical methods, and the results are found to be in excellent agreement with analytic exact solution.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11227-024-06112-x</doi><tpages>31</tpages></addata></record> |
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| subjects | Advection Advection-diffusion equation Compilers Computer Science Exact solutions Finite difference method Interpreters Mathematical analysis Numerical methods Operators (mathematics) Processor Architectures Programming Languages |
| title | Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability |
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