Document Zbl 1504.65176

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Nonlinear Sci. Numer. Simul.</a> <a href="/?q=in%3A491186" title="Articles in this Issue">117, Article ID 106989, 21 p. (2023)</a>. </div> <div class="abstract">Summary: This paper formulates the second-order BDF and theta schemes based on an efficient localized meshless technique for computing the approximate solution of the Sobolev model. The model is one of the useful description for modeling the flow of fluids through fractured rocks, movement of moisture in soils. This proposed approach discretizes the nonlinear Sobolev equation in two main steps. In the first step, temporal discretization is accomplished with the help of the second-order BDF and theta schemes, respectively. In the second step, the localized radial basis function partition of unity collocation method (L-RBF-PUCM) is used for spatial discretization, thereby constructing a fully-discrete algorithm. For large linear problems, global techniques have the disadvantage of high computational cost. The proposed method overcomes this shortcoming well and reduces the computational burden by sparsifying the linear system. The convergence analysis and unconditional stability of the semi-discrete formulation are examined by means of the energy method. Numerical results are carried out to verify the validity and accuracy of the L-RBF-PUCM.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7634612">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65N35" title="MSC2020">65N35</a> </td> <td class="space"> Spectral, collocation and related methods for boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D12" title="MSC2020">65D12</a> </td> <td class="space"> Numerical radial basis function approximation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M12" title="MSC2020">65M12</a> </td> <td class="space"> Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74F10" title="MSC2020">74F10</a> </td> <td class="space"> Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74L10" title="MSC2020">74L10</a> </td> <td class="space"> Soil and rock mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76S05" title="MSC2020">76S05</a> </td> <td class="space"> Flows in porous media; filtration; seepage </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35B35" title="MSC2020">35B35</a> </td> <td class="space"> Stability in context of PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74S20" title="MSC2020">74S20</a> </td> <td class="space"> Finite difference methods applied to problems in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M20" title="MSC2020">76M20</a> </td> <td class="space"> Finite difference methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q74" title="MSC2020">35Q74</a> </td> <td class="space"> PDEs in connection with mechanics of deformable solids </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anonlinear+Sobolev+problem">nonlinear Sobolev problem</a>; <a href="/?q=ut%3Aconvergence+and+stability">convergence and stability</a>; <a href="/?q=ut%3Afinite+difference">finite difference</a>; <a href="/?q=ut%3Atheta-scheme">theta-scheme</a>; <a href="/?q=ut%3Asecond-order+BDF+method">second-order BDF method</a>; <a href="/?q=ut%3Alocal+meshless+technique">local meshless technique</a>; <a href="/?q=ut%3AL-RBF-PUCM">L-RBF-PUCM</a></div> <div class="software"> <h3>Software:</h3><a href="/software/28260">GaussQR</a>; <a href="/software/558">Matlab</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 1504.65176" data-ciurl="/ci/07634612" data-biburl="/bibtex/07634612.bib" data-amsurl="/amsrefs/07634612.bib" data-xmlurl="/xml/07634612.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07634612.pdf" title="Zbl 1504.65176 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/10.1016/j.cnsns.2022.106989" aria-label="DOI for “Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics”" title="10.1016/j.cnsns.2022.106989">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">Abbaszadeh, M.; Dehghan, M., Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation, Appl Numer Math, 154, 172-186 (2020) · <a href="/1437.65174" class="nowrap">Zbl 1437.65174</a></td> </tr><tr> <td>[2]</td> <td class="space">Dehghan, M.; Shafieeabyaneh, N.; Abbaszadeh, M., Numerical and theoretical discussions for solving nonlinear generalized Benjamin-Bona-Mahony-Burgers equation based on the legendre spectral element method, Numer Methods Partial Differ Equ, 37, 360-382 (2021) · <a href="/1535.65130" class="nowrap">Zbl 1535.65130</a></td> </tr><tr> <td>[3]</td> <td class="space">Ewing, R. E., A coupled nonlinear hyperbolic-sobolev system, Ann Math Pur Appl Ser IV, 114, 249-331 (1997)</td> </tr><tr> <td>[4]</td> <td class="space">Showalter, R., Existence and representation theorems for a semilinear Sobolev equation in Banach space, SIAM J Math Anal, 3, 527-543 (1972) · <a href="/0262.34047" class="nowrap">Zbl 0262.34047</a></td> </tr><tr> <td>[5]</td> <td class="space">Ewing, R. E., Numerical solution of Sobolev partial differential equations, SIAM J Numer Anal, 12, 345-363 (1975) · <a href="/0355.65071" class="nowrap">Zbl 0355.65071</a></td> </tr><tr> <td>[6]</td> <td class="space">Gao, F.; Qiu, J.; Zhang, Q., Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation, J Sci Comput, 41, 436-460 (2009) · <a href="/1203.65181" class="nowrap">Zbl 1203.65181</a></td> </tr><tr> <td>[7]</td> <td class="space">Gao, F.; Wang, X., A modified weak Galerkin finite element method for Sobolev equation, J Comput Appl Math, 33, 307-322 (2015) · <a href="/1340.65270" class="nowrap">Zbl 1340.65270</a></td> </tr><tr> <td>[8]</td> <td class="space">Zhao, Z.; Li, H.; Luo, Z., A new space-time continuous Galerkin method with mesh modification for sobolev equations, J Math Anal Appl, 440, 86-105 (2016) · <a href="/1382.65335" class="nowrap">Zbl 1382.65335</a></td> </tr><tr> <td>[9]</td> <td class="space">Luo, Z.; Teng, F.; Chen, J., A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations, Math Comput Simulation, 146, 118-133 (2018) · <a href="/1484.65193" class="nowrap">Zbl 1484.65193</a></td> </tr><tr> <td>[10]</td> <td class="space">Oruç, O., A computational method based on Hermite wavelets for two-dimensional Sobolev and regularized long wave equations in fluids, Numer Methods Part Differ Equ, 34, 1693-1715 (2018) · <a href="/1417.65154" class="nowrap">Zbl 1417.65154</a></td> </tr><tr> <td>[11]</td> <td class="space">Shi, D.; Wang, J.; Yan, F., Unconditional superconvergence analysis of an $H^1$-Galerkin mixed finite element method for nonlinear Sobolev equations, Numer Methods Partial Differ Equ, 34, 145-166 (2018) · <a href="/1390.65120" class="nowrap">Zbl 1390.65120</a></td> </tr><tr> <td>[12]</td> <td class="space">Chen, C.; Li, K.; Chen, Y., Two-grid finite element methods combined with crank-nicolson scheme for nonlinear Sobolev equations, Adv Comput Math, 45, 611-630 (2019) · <a href="/1415.65223" class="nowrap">Zbl 1415.65223</a></td> </tr><tr> <td>[13]</td> <td class="space">Nikan, O.; Avazzadeh, Z., A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics, Appl Math Comput, 401, Article 126063 pp. (2021) · <a href="/1508.65144" class="nowrap">Zbl 1508.65144</a></td> </tr><tr> <td>[14]</td> <td class="space">Mishra, S.; Pany, A. K., Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity, Numer Algorithms, 90, 963-987 (2022) · <a href="/07540325" class="nowrap">Zbl 07540325</a></td> </tr><tr> <td>[15]</td> <td class="space">Zhang, C.; Tang, C., One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay, Commun Nonlinear Sci Numer Simul, 108, Article 106233 pp. (2022) · <a href="/07474634" class="nowrap">Zbl 07474634</a></td> </tr><tr> <td>[16]</td> <td class="space">Zhang, Q.; Qin, Y.; Sun, Z., Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity, Numer Algorithms, 1-34 (2022)</td> </tr><tr> <td>[17]</td> <td class="space">Fasshauer, G. E., Meshfree Approximation Methods with MATLAB, Vol. 6 (2007), World Scientific · <a href="/1123.65001" class="nowrap">Zbl 1123.65001</a></td> </tr><tr> <td>[18]</td> <td class="space">Hardy, R. L., Multiquadric equations of topography and other irregular surfaces, J Geophys Res, 76, 1905-1915 (1971)</td> </tr><tr> <td>[19]</td> <td class="space">Hardy, R. L., Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968-1988, Comput Math Appl, 19, 163-208 (1990) · <a href="/0692.65003" class="nowrap">Zbl 0692.65003</a></td> </tr><tr> <td>[20]</td> <td class="space">Franke, R., Scattered data interpolation: tests of some methods, Math Comp, 38, 181-200 (1982) · <a href="/0476.65005" class="nowrap">Zbl 0476.65005</a></td> </tr><tr> <td>[21]</td> <td class="space">Schaback, R., Error estimates and condition numbers for radial basis function interpolation, Adv Comput Mech, 3, 251-264 (1995) · <a href="/0861.65007" class="nowrap">Zbl 0861.65007</a></td> </tr><tr> <td>[22]</td> <td class="space">Micchelli, C. A., Interpolation of scattered data: distance matrices and conditionally positive definite functions, (Approximation Theory and Spline Functions (1984), Springer), 143-145 · <a href="/0558.41012" class="nowrap">Zbl 0558.41012</a></td> </tr><tr> <td>[23]</td> <td class="space">Kansa, E. J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates, Comput Math Appl, 19, 127-145 (1990) · <a href="/0692.76003" class="nowrap">Zbl 0692.76003</a></td> </tr><tr> <td>[24]</td> <td class="space">Kansa, E. J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput Math Appl, 19, 147-161 (1990) · <a href="/0850.76048" class="nowrap">Zbl 0850.76048</a></td> </tr><tr> <td>[25]</td> <td class="space">Golberg, M.; Chen, C.; Karur, S., Improved multiquadric approximation for partial differential equations, Eng Anal Bound Elem, 18, 9-17 (1996)</td> </tr><tr> <td>[26]</td> <td class="space">Madych, W.; Nelson, S., Multivariate interpolation and conditionally positive definite functions. II, Math Comp, 54, 211-230 (1990) · <a href="/0859.41004" class="nowrap">Zbl 0859.41004</a></td> </tr><tr> <td>[27]</td> <td class="space">Cao, Y.; Nikan, O.; Avazzadeh, Z., A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels, Appl Numer Math, 183, 140-156 (2023) · <a href="/1500.65082" class="nowrap">Zbl 1500.65082</a></td> </tr><tr> <td>[28]</td> <td class="space">Dehghan, M.; Abbaszadeh, M., The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations, J Comput Phys, 351, 478-510 (2017) · <a href="/1380.65301" class="nowrap">Zbl 1380.65301</a></td> </tr><tr> <td>[29]</td> <td class="space">Haq, S.; Hussain, M., Application of meshfree spectral method for the solution of multi-dimensional time-fractional Sobolev equations, Eng Anal Bound Elem, 106, 201-216 (2019) · <a href="/1464.65142" class="nowrap">Zbl 1464.65142</a></td> </tr><tr> <td>[30]</td> <td class="space">Li, M.; Nikan, O.; Qiu, W.; Xu, D., An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows, Eng Anal Bound Elem, 144, 44-54 (2022) · <a href="/1537.76116" class="nowrap">Zbl 1537.76116</a></td> </tr><tr> <td>[31]</td> <td class="space">Mollapourasl, R.; Fereshtian, A.; Li, H.; Lu, X., RBF-PU method for pricing options under the jump-diffusion model with local volatility, J Comput Appl Math, 337, 98-118 (2018) · <a href="/1457.65148" class="nowrap">Zbl 1457.65148</a></td> </tr><tr> <td>[32]</td> <td class="space">Nikan, O.; Avazzadeh, Z.; Machado, J. T., Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics, Eng Anal Bound Elem, 120, 223-237 (2020) · <a href="/1464.65151" class="nowrap">Zbl 1464.65151</a></td> </tr><tr> <td>[33]</td> <td class="space">Nikan, O.; Machado, J.; Avazzadeh, Z.; Jafari, H., Numerical evaluation of fractional tricomi-type model arising from physical problems of gas dynamics, J Adv Res, 25, 205-216 (2020)</td> </tr><tr> <td>[34]</td> <td class="space">Nikan, O.; Machado, J. T.; Golbabai, A., Numerical solution of time-fractional fourth-order reaction-diffusion model arising in composite environments, Appl Math Model, 89, 819-836 (2020) · <a href="/1481.65196" class="nowrap">Zbl 1481.65196</a></td> </tr><tr> <td>[35]</td> <td class="space">Pani, A. K.; Fairweather, G.; Fernandes, R. I., ADI orthogonal spline collocation methods for parabolic partial integro-differential equations, IMA J Numer Anal, 30, 248-276 (2010) · <a href="/1191.65186" class="nowrap">Zbl 1191.65186</a></td> </tr><tr> <td>[36]</td> <td class="space">Sloan, I. H.; Thomee, V., Time discretization of an integro-differential equation of parabolic type, SIAM J Numer Anal, 23, 1052-1061 (1986) · <a href="/0608.65096" class="nowrap">Zbl 0608.65096</a></td> </tr><tr> <td>[37]</td> <td class="space">Qiao, L.; Qiu, W.; Xu, D., A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem, Comput Math Appl, 102, 137-145 (2021) · <a href="/1524.65386" class="nowrap">Zbl 1524.65386</a></td> </tr><tr> <td>[38]</td> <td class="space">Qiao, L.; Xu, D.; Qiu, W., The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space, Appl Numer Math, 172, 359-381 (2022) · <a href="/1484.65345" class="nowrap">Zbl 1484.65345</a></td> </tr><tr> <td>[39]</td> <td class="space">Qiu, W.; Xu, D.; Guo, J., A formally second-order backward differentiation formula sinc-collocation method for the Volterra integro-differential equation with a weakly singular kernel based on the double exponential transformation, Numer Methods Partial Differ Equ, 38, 830-847 (2022) · <a href="/1533.65198" class="nowrap">Zbl 1533.65198</a></td> </tr><tr> <td>[40]</td> <td class="space">Qiu, W.; Xu, D.; Chen, H., A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels, Int J Comput Math, 97, 2055-2073 (2020) · <a href="/1483.65226" class="nowrap">Zbl 1483.65226</a></td> </tr><tr> <td>[41]</td> <td class="space">McLean, W.; Thomée, V., Numerical solution of an evolution equation with a positive-type memory term, J Aust Math Soc Ser B, 35, 23-70 (1993) · <a href="/0791.65105" class="nowrap">Zbl 0791.65105</a></td> </tr><tr> <td>[42]</td> <td class="space">Fasshauer, G. E.; McCourt, M. J., Kernel-Based Approximation Methods using Matlab, Vol. 19 (2015), World Scientific: World Scientific Publishing Company</td> </tr><tr> <td>[43]</td> <td class="space">Fasshauer, G. E.; Zhang, J. G., On choosing optimal shape parameters for rbf approximation, Numer Algorithms, 45, 345-368 (2007) · <a href="/1127.65009" class="nowrap">Zbl 1127.65009</a></td> </tr><tr> <td>[44]</td> <td class="space">Golbabai, A.; Mohebianfar, E.; Rabiei, H., On the new variable shape parameter strategies for radial basis functions, J Comput Appl Math, 34, 691-704 (2015) · <a href="/1322.65040" class="nowrap">Zbl 1322.65040</a></td> </tr><tr> <td>[45]</td> <td class="space">Cavoretto, R.; De Rossi, A.; Mukhametzhanov, M.; Sergeyev, Y. D., On the search of the shape parameter in radial basis functions using univariate global optimization methods, J Global Optim, 1-23 (2019)</td> </tr><tr> <td>[46]</td> <td class="space">Sarra, S. A., A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains, Appl Math Comput, 218, 9853-9865 (2012) · <a href="/1245.65144" class="nowrap">Zbl 1245.65144</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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