An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients
In this paper, we propose a QSC- L 1 method to solve the two-dimensional variable-order time-fractional mobile-immobile diffusion (TF-MID) equations with variably diffusive coefficients, in which the quadratic spline collocation (QSC) method is employed for the spatial discretization, and the classi...
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| Veröffentlicht in: | Journal of scientific computing 2022-11, Vol.93 (2), p.44, Article 44 |
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| creator | Liu, Jun Fu, Hongfei |
| description | In this paper, we propose a QSC-
L
1 method to solve the two-dimensional variable-order time-fractional mobile-immobile diffusion (TF-MID) equations with variably diffusive coefficients, in which the quadratic spline collocation (QSC) method is employed for the spatial discretization, and the classical
L
1 formula is used for the temporal discretization. We show that the method is unconditionally stable and convergent with first-order in time and second-order in space with respect to some discrete and continuous
L
2
norms. Then, combined with the reduced basis technique, an efficient QSC-
L
1-RB method is proposed to improve the computational efficiency. Numerical examples are attached to verify the convergence orders, and also the method is applied to identify parameters of the variable-order TF-MID equations. Numerical results confirm the contributions of the reduced basis technique, even when the observation data is contaminated by some levels of random noise. |
| doi_str_mv | 10.1007/s10915-022-02007-2 |
| format | Article |
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L
1 method to solve the two-dimensional variable-order time-fractional mobile-immobile diffusion (TF-MID) equations with variably diffusive coefficients, in which the quadratic spline collocation (QSC) method is employed for the spatial discretization, and the classical
L
1 formula is used for the temporal discretization. We show that the method is unconditionally stable and convergent with first-order in time and second-order in space with respect to some discrete and continuous
L
2
norms. Then, combined with the reduced basis technique, an efficient QSC-
L
1-RB method is proposed to improve the computational efficiency. Numerical examples are attached to verify the convergence orders, and also the method is applied to identify parameters of the variable-order TF-MID equations. Numerical results confirm the contributions of the reduced basis technique, even when the observation data is contaminated by some levels of random noise.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-022-02007-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Approximation ; Collocation methods ; Computational Mathematics and Numerical Analysis ; Convergence ; Discretization ; Finite element analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Numerical analysis ; Parameter identification ; Random noise ; Theoretical</subject><ispartof>Journal of scientific computing, 2022-11, Vol.93 (2), p.44, Article 44</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor 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><citedby>FETCH-LOGICAL-c249t-f4a35407715b7234e32de30b56fc323b5961dafc008647618be11b0cad1f25b13</citedby><cites>FETCH-LOGICAL-c249t-f4a35407715b7234e32de30b56fc323b5961dafc008647618be11b0cad1f25b13</cites><orcidid>0000-0002-8294-8086</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/s10915-022-02007-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918316850?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Liu, Jun</creatorcontrib><creatorcontrib>Fu, Hongfei</creatorcontrib><title>An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>In this paper, we propose a QSC-
L
1 method to solve the two-dimensional variable-order time-fractional mobile-immobile diffusion (TF-MID) equations with variably diffusive coefficients, in which the quadratic spline collocation (QSC) method is employed for the spatial discretization, and the classical
L
1 formula is used for the temporal discretization. We show that the method is unconditionally stable and convergent with first-order in time and second-order in space with respect to some discrete and continuous
L
2
norms. Then, combined with the reduced basis technique, an efficient QSC-
L
1-RB method is proposed to improve the computational efficiency. Numerical examples are attached to verify the convergence orders, and also the method is applied to identify parameters of the variable-order TF-MID equations. Numerical results confirm the contributions of the reduced basis technique, even when the observation data is contaminated by some levels of random noise.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Collocation methods</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convergence</subject><subject>Discretization</subject><subject>Finite element analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Numerical analysis</subject><subject>Parameter identification</subject><subject>Random noise</subject><subject>Theoretical</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1OwzAQhS0EEqVwAVaWWBv8E8fJsgoFKhVViMLWshMbXDVJa6dAj8CtcRsqdixGHnnee6P5ALgk-JpgLG4CwTnhCFMaK34gegQGhAuGRJqTYzDAWcaRSERyCs5CWGCM8yynA_A9auDYWlc603Tw6bmAo9XKt1-uVp1rG9ha-Kq8U3pp0MxXxsO5qw2686rczdUSPrbaxeGkrvcNvHXWbsLOO15v9iEBfrru_ZCzPSg-DCxac9gdzsGJVctgLn7fIXi5G8-LBzSd3U-K0RSVNMk7ZBPFeIKFIFwLyhLDaGUY1jy1JaNM8zwllbIlxlmaiJRk2hCicakqYinXhA3BVZ8bz1xvTOjkot34eEmQNCcZI2nGcVTRXlX6NgRvrFz5yMRvJcFyh1z2yGVELvfIJY0m1ptCFDdvxv9F_-P6AXKYhSs</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Liu, Jun</creator><creator>Fu, Hongfei</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/0000-0002-8294-8086</orcidid></search><sort><creationdate>20221101</creationdate><title>An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients</title><author>Liu, Jun ; Fu, Hongfei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-f4a35407715b7234e32de30b56fc323b5961dafc008647618be11b0cad1f25b13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Collocation methods</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Convergence</topic><topic>Discretization</topic><topic>Finite element analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Methods</topic><topic>Numerical analysis</topic><topic>Parameter identification</topic><topic>Random noise</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jun</creatorcontrib><creatorcontrib>Fu, Hongfei</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>Liu, Jun</au><au>Fu, Hongfei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2022-11-01</date><risdate>2022</risdate><volume>93</volume><issue>2</issue><spage>44</spage><pages>44-</pages><artnum>44</artnum><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>In this paper, we propose a QSC-
L
1 method to solve the two-dimensional variable-order time-fractional mobile-immobile diffusion (TF-MID) equations with variably diffusive coefficients, in which the quadratic spline collocation (QSC) method is employed for the spatial discretization, and the classical
L
1 formula is used for the temporal discretization. We show that the method is unconditionally stable and convergent with first-order in time and second-order in space with respect to some discrete and continuous
L
2
norms. Then, combined with the reduced basis technique, an efficient QSC-
L
1-RB method is proposed to improve the computational efficiency. Numerical examples are attached to verify the convergence orders, and also the method is applied to identify parameters of the variable-order TF-MID equations. Numerical results confirm the contributions of the reduced basis technique, even when the observation data is contaminated by some levels of random noise.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-022-02007-2</doi><orcidid>https://orcid.org/0000-0002-8294-8086</orcidid></addata></record> |
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| subjects | Algorithms Approximation Collocation methods Computational Mathematics and Numerical Analysis Convergence Discretization Finite element analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numerical analysis Parameter identification Random noise Theoretical |
| title | An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients |
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