High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and st...
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| Veröffentlicht in: | Journal of scientific computing 2017-05, Vol.71 (2), p.759-784 |
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| container_title | Journal of scientific computing |
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| creator | Ding, Hengfei Li, Changpin |
| description | A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and stability for time-dependent problems with Riesz derivatives. In rapid sequence, we apply the 2nd-order formula to one-dimension Riesz spatial fractional partial differential equations to establish an unconditionally stable finite difference scheme with convergent order
O
(
τ
2
+
h
2
)
, where
τ
and
h
are the temporal and spatial stepsizes, respectively. Finally, some numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the derived numerical algorithms. |
| doi_str_mv | 10.1007/s10915-016-0317-3 |
| format | Article |
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O
(
τ
2
+
h
2
)
, where
τ
and
h
are the temporal and spatial stepsizes, respectively. Finally, some numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the derived numerical algorithms.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-016-0317-3</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Accuracy ; Algorithms ; Computational Mathematics and Numerical Analysis ; Convergence ; Derivatives ; Finite difference method ; Fourier transforms ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Partial differential equations ; Theoretical</subject><ispartof>Journal of scientific computing, 2017-05, Vol.71 (2), p.759-784</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Springer Science+Business Media New York 2016.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-aeeef897098555d153b43c1619e9b4764202acef159e275140ca5370e6cc3e763</citedby><cites>FETCH-LOGICAL-c316t-aeeef897098555d153b43c1619e9b4764202acef159e275140ca5370e6cc3e763</cites><orcidid>0000-0003-4044-6499</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/s10915-016-0317-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918312742?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21387,27923,27924,33743,41487,42556,43804,51318,64384,64388,72240</link.rule.ids></links><search><creatorcontrib>Ding, Hengfei</creatorcontrib><creatorcontrib>Li, Changpin</creatorcontrib><title>High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and stability for time-dependent problems with Riesz derivatives. In rapid sequence, we apply the 2nd-order formula to one-dimension Riesz spatial fractional partial differential equations to establish an unconditionally stable finite difference scheme with convergent order
O
(
τ
2
+
h
2
)
, where
τ
and
h
are the temporal and spatial stepsizes, respectively. Finally, some numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the derived numerical algorithms.</description><subject>Accuracy</subject><subject>Algorithms</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convergence</subject><subject>Derivatives</subject><subject>Finite difference method</subject><subject>Fourier transforms</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial differential equations</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEFPwzAMhSMEEmPwA7hF4hyIm6ZpjtNgG9K0SQjOUZa5XaetHUk7BL-ejCJx4mTZfu_Z-gi5BX4PnKuHAFyDZBwyxgUoJs7IAKQSTGUazsmA57lkKlXpJbkKYcs517lOBsTMqnLDln6Nni66PfrK2R0d7crGV-1mH2jRePpSYfiij3F5tG11xECPlaXjpg6t71xb1SVd4AedYo3e_rSTro7zKLgmF4XdBbz5rUPyNnl6Hc_YfDl9Ho_mzAnIWmYRsci1il9JKdcgxSoVDjLQqFepytKEJ9ZhAVJjoiSk3FkpFMfMOYEqE0Ny1-cefPPeYWjNtul8HU-aREMuIFFpElXQq5xvQvBYmIOv9tZ_GuDmxNH0HE3kaE4cjYiepPeEqK1L9H_J_5u-AcNZdYs</recordid><startdate>20170501</startdate><enddate>20170501</enddate><creator>Ding, Hengfei</creator><creator>Li, Changpin</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0003-4044-6499</orcidid></search><sort><creationdate>20170501</creationdate><title>High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions</title><author>Ding, Hengfei ; Li, Changpin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-aeeef897098555d153b43c1619e9b4764202acef159e275140ca5370e6cc3e763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Accuracy</topic><topic>Algorithms</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Convergence</topic><topic>Derivatives</topic><topic>Finite difference method</topic><topic>Fourier transforms</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial differential equations</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ding, Hengfei</creatorcontrib><creatorcontrib>Li, Changpin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ding, Hengfei</au><au>Li, Changpin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2017-05-01</date><risdate>2017</risdate><volume>71</volume><issue>2</issue><spage>759</spage><epage>784</epage><pages>759-784</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and stability for time-dependent problems with Riesz derivatives. In rapid sequence, we apply the 2nd-order formula to one-dimension Riesz spatial fractional partial differential equations to establish an unconditionally stable finite difference scheme with convergent order
O
(
τ
2
+
h
2
)
, where
τ
and
h
are the temporal and spatial stepsizes, respectively. Finally, some numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the derived numerical algorithms.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-016-0317-3</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0003-4044-6499</orcidid></addata></record> |
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| language | eng |
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| source | ProQuest Central UK/Ireland; SpringerLink Journals - AutoHoldings; ProQuest Central |
| subjects | Accuracy Algorithms Computational Mathematics and Numerical Analysis Convergence Derivatives Finite difference method Fourier transforms Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Partial differential equations Theoretical |
| title | High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions |
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