Document Zbl 1522.34028

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Calc. Appl. Anal.</a> <a href="/?q=in%3A503008" title="Articles in this Issue">26, No. 4, 1842-1867 (2023)</a>. </div> <div class="abstract"></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7748687">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34A08" title="MSC2020">34A08</a> </td> <td class="space"> Fractional ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A26A33" title="MSC2020">26A33</a> </td> <td class="space"> Fractional derivatives and integrals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A41A55" title="MSC2020">41A55</a> </td> <td class="space"> Approximate quadratures </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D32" title="MSC2020">65D32</a> </td> <td class="space"> Numerical quadrature and cubature formulas </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconvolution+quadrature">convolution quadrature</a>; <a href="/?q=ut%3Afractional+BT-%5C%28%5Ctheta%5C%29">fractional BT-$\theta$</a>; <a href="/?q=ut%3Afractional+BN-%5C%28%5Ctheta%5C%29">fractional BN-$\theta$</a>; <a href="/?q=ut%3Aa-stable">a-stable</a>; <a href="/?q=ut%3Asuperconvergence">superconvergence</a>; <a href="/?q=ut%3Ainitial+singularity">initial singularity</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1522.34028" data-ciurl="/ci/07748687" data-biburl="/bibtex/07748687.bib" data-amsurl="/amsrefs/07748687.bib" data-xmlurl="/xml/07748687.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07748687.pdf" title="Zbl 1522.34028 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s13540-023-00172-1" aria-label="DOI for “Two families of second-order fractional numerical formulas and applications to fractional differential equations”" title="10.1007/s13540-023-00172-1">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press (1999) · <a href="/0924.34008" class="nowrap">Zbl 0924.34008</a></td> </tr><tr> <td>[2]</td> <td class="space">Lubich, C., Discretized fractional calculus, SIAM J. Math. Anal., 17, 3, 704-719 (1986) · <a href="/0624.65015" class="nowrap">Zbl 0624.65015</a> · <a href="https://doi.org/10.1137/0517050" class="nowrap">doi:10.1137/0517050</a></td> </tr><tr> <td>[3]</td> <td class="space">Jin, B.; Li, B.; Zhou, Z., Correction of high-order BDF convolution quadrature for fractional evolution equations, SIAM J. Sci. Comput., 39, 6, A3129-A3152 (2017) · <a href="/1379.65078" class="nowrap">Zbl 1379.65078</a> · <a href="https://doi.org/10.1137/17M1118816" class="nowrap">doi:10.1137/17M1118816</a></td> </tr><tr> <td>[4]</td> <td class="space">Zeng, F.; Li, C.; Liu, F.; Turner, I., Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy, SIAM J. Sci. Comput., 37, 1, A55-A78 (2015) · <a href="/1334.65162" class="nowrap">Zbl 1334.65162</a> · <a href="https://doi.org/10.1137/14096390X" class="nowrap">doi:10.1137/14096390X</a></td> </tr><tr> <td>[5]</td> <td class="space">Gao, GH; Sun, HW; Sun, ZZ, Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence, J. Comput. Phys., 280, 510-528 (2015) · <a href="/1349.65295" class="nowrap">Zbl 1349.65295</a> · <a href="https://doi.org/10.1016/j.jcp.2014.09.033" class="nowrap">doi:10.1016/j.jcp.2014.09.033</a></td> </tr><tr> <td>[6]</td> <td class="space">Jin, B.; Li, B.; Zhou, Z., An analysis of the Crank-Nicolson method for subdiffusion, IMA J. Numer. Anal., 38, 1, 518-541 (2018) · <a href="/1497.65175" class="nowrap">Zbl 1497.65175</a> · <a href="https://doi.org/10.1093/imanum/drx019" class="nowrap">doi:10.1093/imanum/drx019</a></td> </tr><tr> <td>[7]</td> <td class="space">Alikhanov, AA, A new difference scheme for the time fractional diffusion equation, J. Comput. Phys., 280, 424-438 (2015) · <a href="/1349.65261" class="nowrap">Zbl 1349.65261</a> · <a href="https://doi.org/10.1016/j.jcp.2014.09.031" class="nowrap">doi:10.1016/j.jcp.2014.09.031</a></td> </tr><tr> <td>[8]</td> <td class="space">Liao, HL; McLean, W.; Zhang, J., A second-order scheme with nonuniform time steps for a linear reaction-subdiffusion problem, Commun. Comput. Phys., 30, 2, 567-601 (2021) · <a href="/1473.65110" class="nowrap">Zbl 1473.65110</a> · <a href="https://doi.org/10.4208/cicp.OA-2020-0124" class="nowrap">doi:10.4208/cicp.OA-2020-0124</a></td> </tr><tr> <td>[9]</td> <td class="space">Tian, W.; Zhou, H.; Deng, W., A class of second order difference approximations for solving space fractional diffusion equations, Math. Comput., 84, 294, 1703-1727 (2015) · <a href="/1318.65058" class="nowrap">Zbl 1318.65058</a> · <a href="https://doi.org/10.1090/S0025-5718-2015-02917-2" class="nowrap">doi:10.1090/S0025-5718-2015-02917-2</a></td> </tr><tr> <td>[10]</td> <td class="space">Zeng, F.; Zhang, Z.; Karniadakis, GE, Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions, Comput. Methods Appl. Mech. Eng., 327, 478-502 (2017) · <a href="/1439.65081" class="nowrap">Zbl 1439.65081</a> · <a href="https://doi.org/10.1016/j.cma.2017.08.029" class="nowrap">doi:10.1016/j.cma.2017.08.029</a></td> </tr><tr> <td>[11]</td> <td class="space">Du, Y.; Liu, Y.; Li, H.; Fang, Z.; He, S., Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation, J. Comput. Phys., 344, 108-126 (2017) · <a href="/1380.65258" class="nowrap">Zbl 1380.65258</a> · <a href="https://doi.org/10.1016/j.jcp.2017.04.078" class="nowrap">doi:10.1016/j.jcp.2017.04.078</a></td> </tr><tr> <td>[12]</td> <td class="space">Liu, Y.; Du, YW; Li, H.; Wang, JF, A two-grid finite element approximation for a nonlinear time-fractional Cable equation, Nonlinear Dyn., 85, 2535-2548 (2016) · <a href="/1349.65429" class="nowrap">Zbl 1349.65429</a> · <a href="https://doi.org/10.1007/s11071-016-2843-9" class="nowrap">doi:10.1007/s11071-016-2843-9</a></td> </tr><tr> <td>[13]</td> <td class="space">Wang, Z.; Vong, S., Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation, J. Comput. Phys., 277, 1-15 (2014) · <a href="/1349.65348" class="nowrap">Zbl 1349.65348</a> · <a href="https://doi.org/10.1016/j.jcp.2014.08.012" class="nowrap">doi:10.1016/j.jcp.2014.08.012</a></td> </tr><tr> <td>[14]</td> <td class="space">McLean, W.; Mustapha, K., A second-order accurate numerical method for a fractional wave equation, Numer. Math., 105, 481-510 (2007) · <a href="/1111.65113" class="nowrap">Zbl 1111.65113</a> · <a href="https://doi.org/10.1007/s00211-006-0045-y" class="nowrap">doi:10.1007/s00211-006-0045-y</a></td> </tr><tr> <td>[15]</td> <td class="space">Mustapha, K.; McLean, W., Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations, SIAM J. Numer. Anal., 51, 1, 491-515 (2013) · <a href="/1267.26005" class="nowrap">Zbl 1267.26005</a> · <a href="https://doi.org/10.1137/120880719" class="nowrap">doi:10.1137/120880719</a></td> </tr><tr> <td>[16]</td> <td class="space">Lv, C.; Xu, C., Error analysis of a high order method for time-fractional diffusion equations, SIAM J. Sci. Comput., 38, 5, A2699-A2724 (2016) · <a href="/1348.65123" class="nowrap">Zbl 1348.65123</a> · <a href="https://doi.org/10.1137/15M102664X" class="nowrap">doi:10.1137/15M102664X</a></td> </tr><tr> <td>[17]</td> <td class="space">Li, Z.; Yan, Y.; Ford, NJ, Error estimates of a high order numerical method for solving linear fractional differential equations, Appl. Numer. Math., 114, 201-220 (2017) · <a href="/1357.65089" class="nowrap">Zbl 1357.65089</a> · <a href="https://doi.org/10.1016/j.apnum.2016.04.010" class="nowrap">doi:10.1016/j.apnum.2016.04.010</a></td> </tr><tr> <td>[18]</td> <td class="space">Ding, H.; Li, C., High-order numerical algorithms for Riesz derivatives via constructing new generating functions, J. Sci. Comput., 71, 759-784 (2017) · <a href="/1398.65030" class="nowrap">Zbl 1398.65030</a> · <a href="https://doi.org/10.1007/s10915-016-0317-3" class="nowrap">doi:10.1007/s10915-016-0317-3</a></td> </tr><tr> <td>[19]</td> <td class="space">Zheng, M.; Liu, F.; Turner, I.; Anh, V., A novel high order space-time spectral method for the time fractional Fokker-Planck equation, SIAM J. Sci. Comput., 37, 2, A701-A724 (2015) · <a href="/1320.82052" class="nowrap">Zbl 1320.82052</a> · <a href="https://doi.org/10.1137/140980545" class="nowrap">doi:10.1137/140980545</a></td> </tr><tr> <td>[20]</td> <td class="space">Deng, B.; Zhang, Z.; Zhao, X., Superconvergence points for the spectral interpolation of Riesz fractional derivatives, J. Sci. Comput., 81, 3, 1577-1601 (2019) · <a href="/1434.65292" class="nowrap">Zbl 1434.65292</a> · <a href="https://doi.org/10.1007/s10915-019-01054-6" class="nowrap">doi:10.1007/s10915-019-01054-6</a></td> </tr><tr> <td>[21]</td> <td class="space">Tadjeran, C.; Meerschaert, MM, A second-order accurate numerical method for the two-dimensional fractional diffusion equation, J. Comput. Phys., 220, 2, 813-823 (2007) · <a href="/1113.65124" class="nowrap">Zbl 1113.65124</a> · <a href="https://doi.org/10.1016/j.jcp.2006.05.030" class="nowrap">doi:10.1016/j.jcp.2006.05.030</a></td> </tr><tr> <td>[22]</td> <td class="space">Guo, X.; Li, Y.; Wang, H., A high order finite difference method for tempered fractional diffusion equations with applications to the CGMY model, SIAM J. Sci. Comput., 40, 5, A3322-A3343 (2018) · <a href="/1407.65106" class="nowrap">Zbl 1407.65106</a> · <a href="https://doi.org/10.1137/18M1172739" class="nowrap">doi:10.1137/18M1172739</a></td> </tr><tr> <td>[23]</td> <td class="space">Weilbeer, M.: Efficient numerical methods for fractional differential equations and their analytical background. Ph.D. thesis, Braunschweig, Techn. Univ., Diss., 2005 (2006) · <a href="/1104.26012" class="nowrap">Zbl 1104.26012</a></td> </tr><tr> <td>[24]</td> <td class="space">Liu, Y.; Du, Y.; Li, H.; Liu, F.; Wang, Y., Some second-order $\theta$ schemes combined with finite element method for nonlinear fractional Cable equation, Numer. Algorithms, 80, 533-555 (2019) · <a href="/1433.65218" class="nowrap">Zbl 1433.65218</a> · <a href="https://doi.org/10.1007/s11075-018-0496-0" class="nowrap">doi:10.1007/s11075-018-0496-0</a></td> </tr><tr> <td>[25]</td> <td class="space">Wang, Y.; Liu, Y.; Li, H.; Wang, J., Finite element method combined with second-order time discrete scheme for nonlinear fractional Cable equation, Eur. Phys. J. Plus, 131, 3, 61 (2016) · <a href="https://doi.org/10.1140/epjp/i2016-16061-3" class="nowrap">doi:10.1140/epjp/i2016-16061-3</a></td> </tr><tr> <td>[26]</td> <td class="space">Sun, H.; Sun, ZZ; Gao, GH, Some temporal second order difference schemes for fractional wave equations, Numer. Methods Partial Differ. Equ., 32, 3, 970-1001 (2016) · <a href="/1352.65269" class="nowrap">Zbl 1352.65269</a> · <a href="https://doi.org/10.1002/num.22038" class="nowrap">doi:10.1002/num.22038</a></td> </tr><tr> <td>[27]</td> <td class="space">Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics, vol. 37. Springer Science & Business Media (2010) · <a href="/0957.65001" class="nowrap">Zbl 0957.65001</a></td> </tr><tr> <td>[28]</td> <td class="space">Lubich, C., A stability analysis of convolution quadratures for Abel-Volterra integral equations, IMA J. Numer. Anal., 6, 1, 87-101 (1986) · <a href="/0587.65090" class="nowrap">Zbl 0587.65090</a> · <a href="https://doi.org/10.1093/imanum/6.1.87" class="nowrap">doi:10.1093/imanum/6.1.87</a></td> </tr><tr> <td>[29]</td> <td class="space">Lubich, C., Fractional linear multistep methods for Abel-Volterra integral equations of the second kind, Math. Comput., 45, 172, 463-469 (1985) · <a href="/0584.65090" class="nowrap">Zbl 0584.65090</a> · <a href="https://doi.org/10.1090/S0025-5718-1985-0804935-7" class="nowrap">doi:10.1090/S0025-5718-1985-0804935-7</a></td> </tr><tr> <td>[30]</td> <td class="space">Zeng, F.; Turner, I.; Burrage, K.; Karniadakis, GE, A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations, SIAM J. Sci. Comput., 40, 5, A2986-A3011 (2018) · <a href="/1404.65105" class="nowrap">Zbl 1404.65105</a> · <a href="https://doi.org/10.1137/18M1168169" class="nowrap">doi:10.1137/18M1168169</a></td> </tr><tr> <td>[31]</td> <td class="space">Thomée, V.: Galerkin Finite Element Methods for Parabolic Problems, vol. 25. Springer Science & Business Media (2007) · <a href="/1105.65102" class="nowrap">Zbl 1105.65102</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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