A fourth-order approximation of fractional derivatives with its applications
A new fourth-order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grünwald formulae combining the compact technique. The properties of proposed fractional difference quotient operator are presented and proved. Then the new approx...
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| Veröffentlicht in: | Journal of computational physics 2015-01, Vol.281, p.787-805 |
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| container_title | Journal of computational physics |
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| creator | Hao, Zhao-peng Sun, Zhi-zhong Cao, Wan-rong |
| description | A new fourth-order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grünwald formulae combining the compact technique. The properties of proposed fractional difference quotient operator are presented and proved. Then the new approximation formula is applied to solve the space fractional diffusion equations. By the energy method, the proposed quasi-compact difference scheme is proved to be unconditionally stable and convergent in L2 norm for both 1D and 2D cases. Several numerical examples are given to confirm the theoretical results. |
| doi_str_mv | 10.1016/j.jcp.2014.10.053 |
| format | Article |
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The properties of proposed fractional difference quotient operator are presented and proved. Then the new approximation formula is applied to solve the space fractional diffusion equations. By the energy method, the proposed quasi-compact difference scheme is proved to be unconditionally stable and convergent in L2 norm for both 1D and 2D cases. Several numerical examples are given to confirm the theoretical results.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2014.10.053</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Approximation ; Derivatives ; Diffusion ; Energy methods ; Fractional derivative ; Fractional differential equation ; High-order approximation ; Mathematical analysis ; Mathematical models ; Norms ; Quasi-compact difference scheme ; Two dimensional</subject><ispartof>Journal of computational physics, 2015-01, Vol.281, p.787-805</ispartof><rights>2014 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-a3b355d25c07eecfec456ccb821a81a0a8fdba72e9cc9537e0f5d49aa47e51d83</citedby><cites>FETCH-LOGICAL-c330t-a3b355d25c07eecfec456ccb821a81a0a8fdba72e9cc9537e0f5d49aa47e51d83</cites><orcidid>0000-0003-2980-6166 ; 0000-0003-2994-1368</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0021999114007414$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Hao, Zhao-peng</creatorcontrib><creatorcontrib>Sun, Zhi-zhong</creatorcontrib><creatorcontrib>Cao, Wan-rong</creatorcontrib><title>A fourth-order approximation of fractional derivatives with its applications</title><title>Journal of computational physics</title><description>A new fourth-order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grünwald formulae combining the compact technique. The properties of proposed fractional difference quotient operator are presented and proved. Then the new approximation formula is applied to solve the space fractional diffusion equations. By the energy method, the proposed quasi-compact difference scheme is proved to be unconditionally stable and convergent in L2 norm for both 1D and 2D cases. Several numerical examples are given to confirm the theoretical results.</description><subject>Approximation</subject><subject>Derivatives</subject><subject>Diffusion</subject><subject>Energy methods</subject><subject>Fractional derivative</subject><subject>Fractional differential equation</subject><subject>High-order approximation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Norms</subject><subject>Quasi-compact difference scheme</subject><subject>Two dimensional</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9UMtOwzAQtBBIlMcHcMuRS8o6jpNYnKqKl1SJC5wtd7NWHaV1sNMCf49DOXPax8ysdoaxGw5zDry66-YdDvMCeJnmOUhxwmYcFORFzatTNgMoeK6U4ufsIsYOABpZNjO2WmTW78O4yX1oKWRmGIL_clszOr_LvM1sMDj1ps8S7g4JOFDMPt24ydwYJ0Hv8Jcer9iZNX2k6796yd4fH96Wz_nq9elluVjlKASMuRFrIWVbSISaCC1hKSvEdVNw03ADprHt2tQFKUQlRU1gZVsqY8qaJG8bccluj3fTrx97iqPeuojU92ZHfh81r5uq4KLiKlH5kYrBxxjI6iEkd-Fbc9BTcrrTKTk9JTetUnJJc3_UUPJwcBR0REc7pNYFwlG33v2j_gFNIXhL</recordid><startdate>20150115</startdate><enddate>20150115</enddate><creator>Hao, Zhao-peng</creator><creator>Sun, Zhi-zhong</creator><creator>Cao, Wan-rong</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-2980-6166</orcidid><orcidid>https://orcid.org/0000-0003-2994-1368</orcidid></search><sort><creationdate>20150115</creationdate><title>A fourth-order approximation of fractional derivatives with its applications</title><author>Hao, Zhao-peng ; Sun, Zhi-zhong ; Cao, Wan-rong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-a3b355d25c07eecfec456ccb821a81a0a8fdba72e9cc9537e0f5d49aa47e51d83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Approximation</topic><topic>Derivatives</topic><topic>Diffusion</topic><topic>Energy methods</topic><topic>Fractional derivative</topic><topic>Fractional differential equation</topic><topic>High-order approximation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Norms</topic><topic>Quasi-compact difference scheme</topic><topic>Two dimensional</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hao, Zhao-peng</creatorcontrib><creatorcontrib>Sun, Zhi-zhong</creatorcontrib><creatorcontrib>Cao, Wan-rong</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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 computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hao, Zhao-peng</au><au>Sun, Zhi-zhong</au><au>Cao, Wan-rong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A fourth-order approximation of fractional derivatives with its applications</atitle><jtitle>Journal of computational physics</jtitle><date>2015-01-15</date><risdate>2015</risdate><volume>281</volume><spage>787</spage><epage>805</epage><pages>787-805</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>A new fourth-order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted Grünwald formulae combining the compact technique. 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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Approximation Derivatives Diffusion Energy methods Fractional derivative Fractional differential equation High-order approximation Mathematical analysis Mathematical models Norms Quasi-compact difference scheme Two dimensional |
| title | A fourth-order approximation of fractional derivatives with its applications |
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