Explicit and implicit finite difference schemes for fractional Cattaneo equation
In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a sepa...
Gespeichert in:
| Veröffentlicht in: | Journal of computational physics 2010-09, Vol.229 (19), p.7042-7057 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 7057 |
|---|---|
| container_issue | 19 |
| container_start_page | 7042 |
| container_title | Journal of computational physics |
| container_volume | 229 |
| creator | Ghazizadeh, H.R. Maerefat, M. Azimi, A. |
| description | In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed. |
| doi_str_mv | 10.1016/j.jcp.2010.05.039 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1671500273</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021999110003001</els_id><sourcerecordid>1671500273</sourcerecordid><originalsourceid>FETCH-LOGICAL-c360t-bbbfb7b319127c7f53cdd5b8b8882782cd8221bd141be98c24a5d92e2e7174193</originalsourceid><addsrcrecordid>eNp9kEtLAzEUhYMoWKs_wN1sBDcz5mY6TYIrKfUBBV3oOuRxgynTmTaZiv57M7S4dHU5l3Mf5yPkGmgFFOZ362pttxWjWdOmorU8IROgkpaMw_yUTChlUEop4ZxcpLSmlIpmJibkbfm9bYMNQ6E7V4TNUfjQhQELF7zHiJ3FItlP3GAqfB8LH7UdQt_ptljoYdAd9gXu9nrsXZIzr9uEV8c6JR-Py_fFc7l6fXpZPKxKW8_pUBpjvOGmBgmMW-6b2jrXGGGEEIwLZp1gDIyDGRiUwrKZbpxkyJADn4Gsp-T2sHcb-90e06A2IVls2_GbfVIw59Dk1LzOVjhYbexTiujVNoaNjj8KqBrpqbXK9NRIT9FGZXp55ua4Xier25y4syH9DbIaGgZAs-_-4MOc9StgVMmGEZgLEe2gXB_-ufIL_WGE5g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1671500273</pqid></control><display><type>article</type><title>Explicit and implicit finite difference schemes for fractional Cattaneo equation</title><source>Access via ScienceDirect (Elsevier)</source><creator>Ghazizadeh, H.R. ; Maerefat, M. ; Azimi, A.</creator><creatorcontrib>Ghazizadeh, H.R. ; Maerefat, M. ; Azimi, A.</creatorcontrib><description>In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2010.05.039</identifier><identifier>CODEN: JCTPAH</identifier><language>eng</language><publisher>Kidlington: Elsevier Inc</publisher><subject>Computation ; Computational techniques ; Convergence rate ; Diffusion ; Exact sciences and technology ; Finite difference schemes ; Flux ; Fourier analysis ; Fractional Cattaneo equation ; MacCormack scheme ; Mathematical analysis ; Mathematical methods in physics ; Mathematical models ; Physics ; Predictor-corrector methods ; Stability</subject><ispartof>Journal of computational physics, 2010-09, Vol.229 (19), p.7042-7057</ispartof><rights>2010 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-bbbfb7b319127c7f53cdd5b8b8882782cd8221bd141be98c24a5d92e2e7174193</citedby><cites>FETCH-LOGICAL-c360t-bbbfb7b319127c7f53cdd5b8b8882782cd8221bd141be98c24a5d92e2e7174193</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jcp.2010.05.039$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23152110$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ghazizadeh, H.R.</creatorcontrib><creatorcontrib>Maerefat, M.</creatorcontrib><creatorcontrib>Azimi, A.</creatorcontrib><title>Explicit and implicit finite difference schemes for fractional Cattaneo equation</title><title>Journal of computational physics</title><description>In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.</description><subject>Computation</subject><subject>Computational techniques</subject><subject>Convergence rate</subject><subject>Diffusion</subject><subject>Exact sciences and technology</subject><subject>Finite difference schemes</subject><subject>Flux</subject><subject>Fourier analysis</subject><subject>Fractional Cattaneo equation</subject><subject>MacCormack scheme</subject><subject>Mathematical analysis</subject><subject>Mathematical methods in physics</subject><subject>Mathematical models</subject><subject>Physics</subject><subject>Predictor-corrector methods</subject><subject>Stability</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKs_wN1sBDcz5mY6TYIrKfUBBV3oOuRxgynTmTaZiv57M7S4dHU5l3Mf5yPkGmgFFOZ362pttxWjWdOmorU8IROgkpaMw_yUTChlUEop4ZxcpLSmlIpmJibkbfm9bYMNQ6E7V4TNUfjQhQELF7zHiJ3FItlP3GAqfB8LH7UdQt_ptljoYdAd9gXu9nrsXZIzr9uEV8c6JR-Py_fFc7l6fXpZPKxKW8_pUBpjvOGmBgmMW-6b2jrXGGGEEIwLZp1gDIyDGRiUwrKZbpxkyJADn4Gsp-T2sHcb-90e06A2IVls2_GbfVIw59Dk1LzOVjhYbexTiujVNoaNjj8KqBrpqbXK9NRIT9FGZXp55ua4Xier25y4syH9DbIaGgZAs-_-4MOc9StgVMmGEZgLEe2gXB_-ufIL_WGE5g</recordid><startdate>20100920</startdate><enddate>20100920</enddate><creator>Ghazizadeh, H.R.</creator><creator>Maerefat, M.</creator><creator>Azimi, A.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>IQODW</scope><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></search><sort><creationdate>20100920</creationdate><title>Explicit and implicit finite difference schemes for fractional Cattaneo equation</title><author>Ghazizadeh, H.R. ; Maerefat, M. ; Azimi, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-bbbfb7b319127c7f53cdd5b8b8882782cd8221bd141be98c24a5d92e2e7174193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Computation</topic><topic>Computational techniques</topic><topic>Convergence rate</topic><topic>Diffusion</topic><topic>Exact sciences and technology</topic><topic>Finite difference schemes</topic><topic>Flux</topic><topic>Fourier analysis</topic><topic>Fractional Cattaneo equation</topic><topic>MacCormack scheme</topic><topic>Mathematical analysis</topic><topic>Mathematical methods in physics</topic><topic>Mathematical models</topic><topic>Physics</topic><topic>Predictor-corrector methods</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghazizadeh, H.R.</creatorcontrib><creatorcontrib>Maerefat, M.</creatorcontrib><creatorcontrib>Azimi, A.</creatorcontrib><collection>Pascal-Francis</collection><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>Ghazizadeh, H.R.</au><au>Maerefat, M.</au><au>Azimi, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Explicit and implicit finite difference schemes for fractional Cattaneo equation</atitle><jtitle>Journal of computational physics</jtitle><date>2010-09-20</date><risdate>2010</risdate><volume>229</volume><issue>19</issue><spage>7042</spage><epage>7057</epage><pages>7042-7057</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><coden>JCTPAH</coden><abstract>In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.</abstract><cop>Kidlington</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2010.05.039</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9991 |
| ispartof | Journal of computational physics, 2010-09, Vol.229 (19), p.7042-7057 |
| issn | 0021-9991 1090-2716 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1671500273 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Computation Computational techniques Convergence rate Diffusion Exact sciences and technology Finite difference schemes Flux Fourier analysis Fractional Cattaneo equation MacCormack scheme Mathematical analysis Mathematical methods in physics Mathematical models Physics Predictor-corrector methods Stability |
| title | Explicit and implicit finite difference schemes for fractional Cattaneo equation |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T11%3A37%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Explicit%20and%20implicit%20finite%20difference%20schemes%20for%20fractional%20Cattaneo%20equation&rft.jtitle=Journal%20of%20computational%20physics&rft.au=Ghazizadeh,%20H.R.&rft.date=2010-09-20&rft.volume=229&rft.issue=19&rft.spage=7042&rft.epage=7057&rft.pages=7042-7057&rft.issn=0021-9991&rft.eissn=1090-2716&rft.coden=JCTPAH&rft_id=info:doi/10.1016/j.jcp.2010.05.039&rft_dat=%3Cproquest_cross%3E1671500273%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1671500273&rft_id=info:pmid/&rft_els_id=S0021999110003001&rfr_iscdi=true |