Krämer, Patrick; Schratz, Katharina; Zhao, Xiaofei Splitting methods for nonlinear Dirac equations with Thirring type interaction in the nonrelativistic limit regime. (English) Zbl 07305177 J. Comput. Appl. Math. 387, Article ID 112494, 16 p. (2021). MSC: 78A35 78M20 78M22 65M06 65N35 65M12 65M15 81Q05 35Q41 PDF BibTeX XML Cite \textit{P. Krämer} et al., J. Comput. Appl. Math. 387, Article ID 112494, 16 p. (2021; Zbl 07305177) Full Text: DOI
Pani, Amiya K.; Thomée, Vidar; Vasudeva Murthy, A. S. A first-order explicit-implicit splitting method for a convection-diffusion problem. (English) Zbl 07284951 Comput. Methods Appl. Math. 20, No. 4, 769-782 (2020). Reviewer: Qifeng Zhang (Hangzhou) MSC: 65M06 65M15 35K10 PDF BibTeX XML Cite \textit{A. K. Pani} et al., Comput. Methods Appl. Math. 20, No. 4, 769--782 (2020; Zbl 07284951) Full Text: DOI
Suzuki, Yuya; Nuyens, Dirk Rank-1 lattices and higher-order exponential splitting for the time-dependent Schrödinger equation. (English) Zbl 07240110 Tuffin, Bruno (ed.) et al., Monte Carlo and quasi-Monte Carlo methods. MCQMC 2018. Proceedings of the 13th international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing, Rennes, France, July 1–6, 2018. Cham: Springer (ISBN 978-3-030-43464-9/hbk; 978-3-030-43465-6/ebook). Springer Proceedings in Mathematics & Statistics 324, 485-502 (2020). MSC: 65C05 PDF BibTeX XML Cite \textit{Y. Suzuki} and \textit{D. Nuyens}, in: Monte Carlo and quasi-Monte Carlo methods. MCQMC 2018. Proceedings of the 13th international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing, Rennes, France, July 1--6, 2018. Cham: Springer. 485--502 (2020; Zbl 07240110) Full Text: DOI
Acebrón, Juan A.; Herrero, José R.; Monteiro, José A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method. (English) Zbl 1451.65056 Comput. Math. Appl. 79, No. 12, 3495-3515 (2020). MSC: 65F60 65Y05 65C05 PDF BibTeX XML Cite \textit{J. A. Acebrón} et al., Comput. Math. Appl. 79, No. 12, 3495--3515 (2020; Zbl 1451.65056) Full Text: DOI
Bertoli, Guillaume; Vilmart, Gilles Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity. (English) Zbl 1447.65058 SIAM J. Sci. Comput. 42, No. 3, A1913-A1934 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65M20 65M12 65L04 35K58 35K57 PDF BibTeX XML Cite \textit{G. Bertoli} and \textit{G. Vilmart}, SIAM J. Sci. Comput. 42, No. 3, A1913--A1934 (2020; Zbl 1447.65058) Full Text: DOI
Hochbruck, Marlis; Leibold, Jan; Ostermann, Alexander On the convergence of Lawson methods for semilinear stiff problems. (English) Zbl 1453.65269 Numer. Math. 145, No. 3, 553-580 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 65M12 65M15 65J08 65L04 65L06 35Q41 PDF BibTeX XML Cite \textit{M. Hochbruck} et al., Numer. Math. 145, No. 3, 553--580 (2020; Zbl 1453.65269) Full Text: DOI
Bao, Weizhu; Cai, Yongyong; Yin, Jia Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. (English) Zbl 1440.35286 Math. Comput. 89, No. 325, 2141-2173 (2020). MSC: 35Q41 65M70 65N35 81Q05 PDF BibTeX XML Cite \textit{W. Bao} et al., Math. Comput. 89, No. 325, 2141--2173 (2020; Zbl 1440.35286) Full Text: DOI
Acebrón, Juan A. A probabilistic linear solver based on a multilevel Monte Carlo method. (English) Zbl 07174119 J. Sci. Comput. 82, No. 3, Paper No. 65, 22 p. (2020). MSC: 65C 65F PDF BibTeX XML Cite \textit{J. A. Acebrón}, J. Sci. Comput. 82, No. 3, Paper No. 65, 22 p. (2020; Zbl 07174119) Full Text: DOI
Padgett, Joshua L.; Sheng, Qin Convergence of an operator splitting scheme for abstract stochastic evolution equations. (English) Zbl 1445.65004 Singh, Vinai K. (ed.) et al., Advances in mathematical methods and high performance computing. Cham: Springer. Adv. Mech. Math. 41, 163-179 (2019). MSC: 65C30 60H15 PDF BibTeX XML Cite \textit{J. L. Padgett} and \textit{Q. Sheng}, Adv. Mech. Math. 41, 163--179 (2019; Zbl 1445.65004) Full Text: DOI
Suzuki, Yuya; Suryanarayana, Gowri; Nuyens, Dirk Strang splitting in combination with rank-1 and rank-\(r\) lattices for the time-dependent Schrödinger equation. (English) Zbl 07131261 SIAM J. Sci. Comput. 41, No. 6, B1254-B1283 (2019). MSC: 65M15 65M70 65T40 35Q41 PDF BibTeX XML Cite \textit{Y. Suzuki} et al., SIAM J. Sci. Comput. 41, No. 6, B1254--B1283 (2019; Zbl 07131261) Full Text: DOI arXiv
Zhai, Shuying; Wang, Dongling; Weng, Zhifeng; Zhao, Xuan Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation. (English) Zbl 07129384 J. Sci. Comput. 81, No. 2, 965-989 (2019). MSC: 65M70 65M12 65M15 35Q55 35R11 PDF BibTeX XML Cite \textit{S. Zhai} et al., J. Sci. Comput. 81, No. 2, 965--989 (2019; Zbl 07129384) Full Text: DOI
Thomée, Vidar; Vasudeva Murthy, A. S. An explicit-implicit splitting method for a convection-diffusion problem. (English) Zbl 1420.65089 Comput. Methods Appl. Math. 19, No. 2, 283-293 (2019). MSC: 65M06 35K10 65M15 86A10 PDF BibTeX XML Cite \textit{V. Thomée} and \textit{A. S. Vasudeva Murthy}, Comput. Methods Appl. Math. 19, No. 2, 283--293 (2019; Zbl 1420.65089) Full Text: DOI
Drawert, Brian; Jacob, Bruno; Li, Zhen; Yi, Tau-Mu; Petzold, Linda A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection-diffusion-reaction problems. (English) Zbl 1416.76244 J. Comput. Phys. 378, 1-17 (2019). MSC: 76M28 76R50 92C37 65M75 PDF BibTeX XML Cite \textit{B. Drawert} et al., J. Comput. Phys. 378, 1--17 (2019; Zbl 1416.76244) Full Text: DOI
Zürnaci, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, Gamze Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting. (English) Zbl 1424.35310 Turk. J. Math. 42, No. 3, 1471-1483 (2018). MSC: 35Q53 65J08 PDF BibTeX XML Cite \textit{F. Zürnaci} et al., Turk. J. Math. 42, No. 3, 1471--1483 (2018; Zbl 1424.35310) Full Text: DOI
Celledoni, Elena; Høiseth, Eirik Hoel; Ramzina, Nataliya Passivity-preserving splitting methods for rigid body systems. (English) Zbl 1407.93244 Multibody Syst. Dyn. 44, No. 3, 251-275 (2018). MSC: 93C85 70Q05 70E60 PDF BibTeX XML Cite \textit{E. Celledoni} et al., Multibody Syst. Dyn. 44, No. 3, 251--275 (2018; Zbl 1407.93244) Full Text: DOI
Csomós, Petra; Mena, Hermann Fourier-splitting method for solving hyperbolic LQR problems. (English) Zbl 1406.35449 Numer. Algebra Control Optim. 8, No. 1, 17-46 (2018). MSC: 35Q93 49J20 65M22 93B52 34H05 76B15 93C20 93C15 65T50 65F30 PDF BibTeX XML Cite \textit{P. Csomós} and \textit{H. Mena}, Numer. Algebra Control Optim. 8, No. 1, 17--46 (2018; Zbl 1406.35449) Full Text: DOI
Lukassen, Axel Ariaan; Kiehl, Martin Operator splitting for chemical reaction systems with fast chemistry. (English) Zbl 06910433 J. Comput. Appl. Math. 344, 495-511 (2018). MSC: 65 92 PDF BibTeX XML Cite \textit{A. A. Lukassen} and \textit{M. Kiehl}, J. Comput. Appl. Math. 344, 495--511 (2018; Zbl 06910433) Full Text: DOI
Zhan, Rui; Zhao, Jingjun The analysis of operator splitting methods for the Camassa-Holm equation. (English) Zbl 1393.65018 Appl. Numer. Math. 130, 1-22 (2018). MSC: 65M06 65M12 35Q35 76B15 22E70 76B25 35Q53 PDF BibTeX XML Cite \textit{R. Zhan} and \textit{J. Zhao}, Appl. Numer. Math. 130, 1--22 (2018; Zbl 1393.65018) Full Text: DOI
Grohs, Philipp; Hiptmair, Ralf; Pintarelli, Simon Tensor-product discretization for the spatially inhomogeneous and transient Boltzmann equation in two dimensions. (English) Zbl 1416.82038 SMAI J. Comput. Math. 3, 219-248 (2017). MSC: 82C80 65M60 45K05 76P05 82C40 PDF BibTeX XML Cite \textit{P. Grohs} et al., SMAI J. Comput. Math. 3, 219--248 (2017; Zbl 1416.82038) Full Text: DOI
Lee, Hyun Geun A semi-analytical Fourier spectral method for the Swift-Hohenberg equation. (English) Zbl 1397.65205 Comput. Math. Appl. 74, No. 8, 1885-1896 (2017). MSC: 65M70 65M12 35Q35 35C05 PDF BibTeX XML Cite \textit{H. G. Lee}, Comput. Math. Appl. 74, No. 8, 1885--1896 (2017; Zbl 1397.65205) Full Text: DOI
Caliari, M.; Ostermann, A.; Piazzola, C. A splitting approach for the magnetic Schrödinger equation. (English) Zbl 1373.81195 J. Comput. Appl. Math. 316, 74-85 (2017). MSC: 81Q05 78A25 42B05 42B10 65T50 81T80 PDF BibTeX XML Cite \textit{M. Caliari} et al., J. Comput. Appl. Math. 316, 74--85 (2017; Zbl 1373.81195) Full Text: DOI
Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub A second-order operator splitting Fourier spectral method for models of epitaxial thin film growth. (English) Zbl 1372.35240 J. Sci. Comput. 71, No. 3, 1303-1318 (2017). MSC: 35Q35 65M12 65M70 76A20 PDF BibTeX XML Cite \textit{H. G. Lee} et al., J. Sci. Comput. 71, No. 3, 1303--1318 (2017; Zbl 1372.35240) Full Text: DOI
Csomós, Petra; Mena, Hermann Innovative integrators for computing the optimal state in LQR problems. (English) Zbl 1368.65095 Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 269-276 (2017). MSC: 65K10 49J20 49M25 49N10 PDF BibTeX XML Cite \textit{P. Csomós} and \textit{H. Mena}, Lect. Notes Comput. Sci. 10187, 269--276 (2017; Zbl 1368.65095) Full Text: DOI
Auzinger, Winfried; Koch, Othmar; Quell, Michael Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. (English) Zbl 1365.65212 Numer. Algorithms 75, No. 1, 261-283 (2017). MSC: 65M20 35K55 65L05 65M12 65M15 PDF BibTeX XML Cite \textit{W. Auzinger} et al., Numer. Algorithms 75, No. 1, 261--283 (2017; Zbl 1365.65212) Full Text: DOI arXiv
Gücüyenen, Nurcan Strang splitting method to Benjamin-Bona-Mahony type equations: analysis and application. (English) Zbl 1357.65119 J. Comput. Appl. Math. 318, 616-623 (2017). MSC: 65M06 35Q53 65M12 PDF BibTeX XML Cite \textit{N. Gücüyenen}, J. Comput. Appl. Math. 318, 616--623 (2017; Zbl 1357.65119) Full Text: DOI
Çiçek, Y.; Tanoǧlu, G. Strang splitting method for Burgers-Huxley equation. (English) Zbl 1410.65206 Appl. Math. Comput. 276, 454-467 (2016). MSC: 65J08 35Q53 PDF BibTeX XML Cite \textit{Y. Çiçek} and \textit{G. Tanoǧlu}, Appl. Math. Comput. 276, 454--467 (2016; Zbl 1410.65206) Full Text: DOI
Hansen, Eskil; Ostermann, Alexander High-order splitting schemes for semilinear evolution equations. (English) Zbl 1355.65071 BIT 56, No. 4, 1303-1316 (2016). MSC: 65J08 65L04 34G20 35K58 35K57 35L70 65M12 65M15 65L06 65L20 PDF BibTeX XML Cite \textit{E. Hansen} and \textit{A. Ostermann}, BIT 56, No. 4, 1303--1316 (2016; Zbl 1355.65071) Full Text: DOI
Vikulova, Nathalie A.; Katsnelson, Leonid B.; Kursanov, Alexander G.; Solovyova, Olga; Markhasin, Vladimir S. Mechano-electric feedback in one-dimensional model of myocardium. (English) Zbl 1343.92041 J. Math. Biol. 73, No. 2, 335-366 (2016). MSC: 92C05 92C30 92B25 PDF BibTeX XML Cite \textit{N. A. Vikulova} et al., J. Math. Biol. 73, No. 2, 335--366 (2016; Zbl 1343.92041) Full Text: DOI
Eilinghoff, Johannes; Schnaubelt, Roland; Schratz, Katharina Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation. (English) Zbl 1339.65152 J. Math. Anal. Appl. 442, No. 2, 740-760 (2016). MSC: 65M15 65M06 65M12 35Q55 PDF BibTeX XML Cite \textit{J. Eilinghoff} et al., J. Math. Anal. Appl. 442, No. 2, 740--760 (2016; Zbl 1339.65152) Full Text: DOI
Pavlova, Jevgenija; Fasano, Antonio; Sequeira, Adélia Numerical simulations of a reduced model for blood coagulation. (English) Zbl 1341.92016 Z. Angew. Math. Phys. 67, No. 2, Article ID 28, 20 p. (2016). MSC: 92C35 76Z05 PDF BibTeX XML Cite \textit{J. Pavlova} et al., Z. Angew. Math. Phys. 67, No. 2, Article ID 28, 20 p. (2016; Zbl 1341.92016) Full Text: DOI
Blanes, Sergio; Casas, Fernando; Murua, Ander An efficient algorithm based on splitting for the time integration of the Schrödinger equation. (English) Zbl 1349.65393 J. Comput. Phys. 303, 396-412 (2015). MSC: 65M20 65L04 PDF BibTeX XML Cite \textit{S. Blanes} et al., J. Comput. Phys. 303, 396--412 (2015; Zbl 1349.65393) Full Text: DOI
Pavlova, J.; Fasano, A.; Janela, J.; Sequeira, A. Numerical validation of a synthetic cell-based model of blood coagulation. (English) Zbl 1343.92113 J. Theor. Biol. 380, 367-379 (2015). MSC: 92C35 76Z05 92C40 PDF BibTeX XML Cite \textit{J. Pavlova} et al., J. Theor. Biol. 380, 367--379 (2015; Zbl 1343.92113) Full Text: DOI
Kieri, Emil Stiff convergence of force-gradient operator splitting methods. (English) Zbl 1325.65075 Appl. Numer. Math. 94, 33-45 (2015). MSC: 65J08 35Q41 35K10 35K90 PDF BibTeX XML Cite \textit{E. Kieri}, Appl. Numer. Math. 94, 33--45 (2015; Zbl 1325.65075) Full Text: DOI
Einkemmer, Lukas; Ostermann, Alexander An almost symmetric Strang splitting scheme for nonlinear evolution equations. (English) Zbl 1368.65074 Comput. Math. Appl. 67, No. 12, 2144-2157 (2014). MSC: 65J08 35F20 65M12 PDF BibTeX XML Cite \textit{L. Einkemmer} and \textit{A. Ostermann}, Comput. Math. Appl. 67, No. 12, 2144--2157 (2014; Zbl 1368.65074) Full Text: DOI
Suárez, Pablo U.; Morales, J. Héctor Fourier splitting method for Kawahara type equations. (English) Zbl 1303.65088 J. Comput. Methods Phys. 2014, Article ID 894956, 4 p. (2014). MSC: 65M70 35Q51 PDF BibTeX XML Cite \textit{P. U. Suárez} and \textit{J. H. Morales}, J. Comput. Methods Phys. 2014, Article ID 894956, 4 p. (2014; Zbl 1303.65088) Full Text: DOI
Petersen, Wesley P.; Vuillermot, Pierre A. Product approximations for a class of quantum anharmonic oscillators. (English) Zbl 1298.81081 Z. Angew. Math. Phys. 65, No. 4, 613-643 (2014). MSC: 81Q05 81Q10 34L40 65L60 PDF BibTeX XML Cite \textit{W. P. Petersen} and \textit{P. A. Vuillermot}, Z. Angew. Math. Phys. 65, No. 4, 613--643 (2014; Zbl 1298.81081) Full Text: DOI
Hellander, Andreas; Lawson, Michael J.; Drawert, Brian; Petzold, Linda Local error estimates for adaptive simulation of the reaction-diffusion master equation via operator splitting. (English) Zbl 1296.65121 J. Comput. Phys. 266, 89-100 (2014). MSC: 65M15 65M06 35K57 PDF BibTeX XML Cite \textit{A. Hellander} et al., J. Comput. Phys. 266, 89--100 (2014; Zbl 1296.65121) Full Text: DOI arXiv
Auzinger, Winfried; Koch, Othmar; Thalhammer, Mechthild Defect-based local error estimators for splitting methods, with application to Schrödinger equations. II: Higher-order methods for linear problems. (English) Zbl 1291.65282 J. Comput. Appl. Math. 255, 384-403 (2014). MSC: 65M15 65M12 35Q41 65J10 PDF BibTeX XML Cite \textit{W. Auzinger} et al., J. Comput. Appl. Math. 255, 384--403 (2014; Zbl 1291.65282) Full Text: DOI
Blanes, S.; Casas, F.; Chartier, P.; Murua, A. Optimized high-order splitting methods for some classes of parabolic equations. (English) Zbl 1278.65075 Math. Comput. 82, No. 283, 1559-1576 (2013). Reviewer: Krzysztof Moszyński (Warszawa) MSC: 65J08 47D06 65L05 34G10 PDF BibTeX XML Cite \textit{S. Blanes} et al., Math. Comput. 82, No. 283, 1559--1576 (2013; Zbl 1278.65075) Full Text: DOI
Shen, Jie; Wang, Zhong-Qing Error analysis of the Strang time-splitting Laguerre-Hermite/Hermite collocation methods for the Gross-Pitaevskii equation. (English) Zbl 1264.65168 Found. Comput. Math. 13, No. 1, 99-137 (2013). Reviewer: Marius Ghergu (Dublin) MSC: 65M70 65M15 35Q35 PDF BibTeX XML Cite \textit{J. Shen} and \textit{Z.-Q. Wang}, Found. Comput. Math. 13, No. 1, 99--137 (2013; Zbl 1264.65168) Full Text: DOI
Holden, Helge; Lubich, Christian; Risebro, Nils Henrik Operator splitting for partial differential equations with Burgers nonlinearity. (English) Zbl 1260.35184 Math. Comput. 82, No. 281, 173-185 (2013). MSC: 35Q53 65M12 65M15 PDF BibTeX XML Cite \textit{H. Holden} et al., Math. Comput. 82, No. 281, 173--185 (2013; Zbl 1260.35184) Full Text: DOI arXiv
Teufel, Stefan; Wachsmuth, Jakob Spontaneous decay of resonant energy levels for molecules with moving nuclei. (English) Zbl 1256.81121 Commun. Math. Phys. 315, No. 3, 699-738 (2012). MSC: 81V55 81Q05 81V80 PDF BibTeX XML Cite \textit{S. Teufel} and \textit{J. Wachsmuth}, Commun. Math. Phys. 315, No. 3, 699--738 (2012; Zbl 1256.81121) Full Text: DOI arXiv
Ostermann, Alexander; Schratz, Katharina Error analysis of splitting methods for inhomogeneous evolution equations. (English) Zbl 1267.65085 Appl. Numer. Math. 62, No. 10, 1436-1446 (2012). Reviewer: Thomas Sonar (Braunschweig) MSC: 65L05 34G20 35K90 65L70 PDF BibTeX XML Cite \textit{A. Ostermann} and \textit{K. Schratz}, Appl. Numer. Math. 62, No. 10, 1436--1446 (2012; Zbl 1267.65085) Full Text: DOI
Hansen, Eskil; Kramer, Felix; Ostermann, Alexander A second-order positivity preserving scheme for semilinear parabolic problems. (English) Zbl 1267.65082 Appl. Numer. Math. 62, No. 10, 1428-1435 (2012). Reviewer: Thomas Sonar (Braunschweig) MSC: 65L05 34G20 35K90 35K58 65L20 PDF BibTeX XML Cite \textit{E. Hansen} et al., Appl. Numer. Math. 62, No. 10, 1428--1435 (2012; Zbl 1267.65082) Full Text: DOI
Auzinger, Winfried; Koch, Othmar; Thalhammer, Mechthild Defect-based local error estimators for splitting methods, with application to Schrödinger equations. I: The linear case. (English) Zbl 1238.65091 J. Comput. Appl. Math. 236, No. 10, 2643-2659 (2012). MSC: 65M15 35Q41 65M99 PDF BibTeX XML Cite \textit{W. Auzinger} et al., J. Comput. Appl. Math. 236, No. 10, 2643--2659 (2012; Zbl 1238.65091) Full Text: DOI
Baudouin, Lucie; Salomon, Julien; Turinici, Gabriel Analysis of the “toolkit” method for the time-dependent Schrödinger equation. (English) Zbl 1274.65231 J. Sci. Comput. 49, No. 2, 111-136 (2011). MSC: 65M06 PDF BibTeX XML Cite \textit{L. Baudouin} et al., J. Sci. Comput. 49, No. 2, 111--136 (2011; Zbl 1274.65231) Full Text: DOI
Faou, Erwan; Grébert, Benoît Hamiltonian interpolation of splitting approximations for nonlinear PDEs. (English) Zbl 1232.65176 Found. Comput. Math. 11, No. 4, 381-415 (2011). Reviewer: T. C. Mohan (Dehra Dun) MSC: 65P10 37M15 35L70 PDF BibTeX XML Cite \textit{E. Faou} and \textit{B. Grébert}, Found. Comput. Math. 11, No. 4, 381--415 (2011; Zbl 1232.65176) Full Text: DOI
Geiser, Jürgen Computing exponential for iterative splitting methods: algorithms and applications. (English) Zbl 1217.65065 J. Appl. Math. 2011, Article ID 193781, 27 p. (2011). MSC: 65F10 15A16 PDF BibTeX XML Cite \textit{J. Geiser}, J. Appl. Math. 2011, Article ID 193781, 27 p. (2011; Zbl 1217.65065) Full Text: DOI EuDML
Bátkai, András; Csomós, Petra; Farkas, Bálint; Nickel, Gregor Operator splitting for non-autonomous evolution equations. (English) Zbl 1232.65103 J. Funct. Anal. 260, No. 7, 2163-2190 (2011). Reviewer: Hector O. Fattorini (Los Angeles) MSC: 65L05 34G10 47D06 PDF BibTeX XML Cite \textit{A. Bátkai} et al., J. Funct. Anal. 260, No. 7, 2163--2190 (2011; Zbl 1232.65103) Full Text: DOI arXiv
Jüngel, Ansgar; Mennemann, Jan-Frederik Time-dependent simulations of quantum waveguides using a time-splitting spectral method. (English) Zbl 1205.81091 Math. Comput. Simul. 81, No. 4, 883-898 (2010). MSC: 81Q37 81Q05 65M70 35Q41 37N20 81T80 82D77 PDF BibTeX XML Cite \textit{A. Jüngel} and \textit{J.-F. Mennemann}, Math. Comput. Simul. 81, No. 4, 883--898 (2010; Zbl 1205.81091) Full Text: DOI
Jahnke, Tobias; Altıntan, Derya Efficient simulation of discrete stochastic reaction systems with a splitting method. (English) Zbl 1205.65023 BIT 50, No. 4, 797-822 (2010). MSC: 65C30 60H10 60H35 34F05 60J75 65L70 47D06 92C42 PDF BibTeX XML Cite \textit{T. Jahnke} and \textit{D. Altıntan}, BIT 50, No. 4, 797--822 (2010; Zbl 1205.65023) Full Text: DOI
Descombes, Stéphane; Thalhammer, Mechthild An exact local error representation of exponential operator splitting methods for evolutionary problems and applications to linear Schrödinger equations in the semi-classical regime. (English) Zbl 1205.65250 BIT 50, No. 4, 729-749 (2010). MSC: 65M15 35Q40 81Q05 35K20 65M06 65M12 PDF BibTeX XML Cite \textit{S. Descombes} and \textit{M. Thalhammer}, BIT 50, No. 4, 729--749 (2010; Zbl 1205.65250) Full Text: DOI
Huhtanen, Marko Matrix subspaces and determinantal hypersurfaces. (English) Zbl 1191.15010 Ark. Mat. 48, No. 1, 57-77 (2010). Reviewer: Jorma K. Merikoski (Tampere) MSC: 15A23 15A09 15A12 15A30 PDF BibTeX XML Cite \textit{M. Huhtanen}, Ark. Mat. 48, No. 1, 57--77 (2010; Zbl 1191.15010) Full Text: DOI
Geiser, Jürgen Consistency of iterative operator-splitting methods: theory and applications. (English) Zbl 1425.65129 Numer. Methods Partial Differ. Equations 26, No. 1, 135-158 (2010). MSC: 65M99 35Q35 35K57 65M15 PDF BibTeX XML Cite \textit{J. Geiser}, Numer. Methods Partial Differ. Equations 26, No. 1, 135--158 (2010; Zbl 1425.65129) Full Text: DOI
Hansen, Eskil; Ostermann, Alexander Exponential splitting for unbounded operators. (English) Zbl 1198.65185 Math. Comput. 78, No. 267, 1485-1496 (2009). MSC: 65M15 65J10 65L05 35Q40 PDF BibTeX XML Cite \textit{E. Hansen} and \textit{A. Ostermann}, Math. Comput. 78, No. 267, 1485--1496 (2009; Zbl 1198.65185) Full Text: DOI
Faou, Erwan Analysis of splitting methods for reaction-diffusion problems using stochastic calculus. (English) Zbl 1198.65184 Math. Comput. 78, No. 267, 1467-1483 (2009). MSC: 65M15 60H30 65C05 PDF BibTeX XML Cite \textit{E. Faou}, Math. Comput. 78, No. 267, 1467--1483 (2009; Zbl 1198.65184) Full Text: DOI
Castella, François; Dujardin, Guillaume Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation. (English) Zbl 1171.65089 ESAIM, Math. Model. Numer. Anal. 43, No. 4, 651 (2009). Reviewer: Qin Mengzhao (Beijing) MSC: 65P10 37K55 37M15 35J10 PDF BibTeX XML Cite \textit{F. Castella} and \textit{G. Dujardin}, ESAIM, Math. Model. Numer. Anal. 43, No. 4, 651 (2009; Zbl 1171.65089) Full Text: DOI EuDML
Neuhauser, Christof; Thalhammer, Mechthild On the convergence of splitting methods for linear evolutionary Schrödinger equations involving an unbounded potential. (English) Zbl 1162.65385 BIT 49, No. 1, 199-215 (2009). MSC: 65M20 65M12 65M15 35Q40 PDF BibTeX XML Cite \textit{C. Neuhauser} and \textit{M. Thalhammer}, BIT 49, No. 1, 199--215 (2009; Zbl 1162.65385) Full Text: DOI
Kube, Susanna; Lasser, Caroline; Weber, Marcus Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics. (English) Zbl 1161.81394 J. Comput. Phys. 228, No. 6, 1947-1962 (2009). MSC: 81S30 65C05 65D30 PDF BibTeX XML Cite \textit{S. Kube} et al., J. Comput. Phys. 228, No. 6, 1947--1962 (2009; Zbl 1161.81394) Full Text: DOI
Sørevik, Tor; Birkeland, Tore; Okša, Gabriel Numerical solution of the 3D time dependent Schrödinger equation in spherical coordinates: Spectral basis and effects of split-operator technique. (English) Zbl 1159.65349 J. Comput. Appl. Math. 225, No. 1, 56-67 (2009). MSC: 65M70 35Q40 81V05 PDF BibTeX XML Cite \textit{T. Sørevik} et al., J. Comput. Appl. Math. 225, No. 1, 56--67 (2009; Zbl 1159.65349) Full Text: DOI
Lubich, Christian On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations. (English) Zbl 1198.65186 Math. Comput. 77, No. 264, 2141-2153 (2008). MSC: 65M15 PDF BibTeX XML Cite \textit{C. Lubich}, Math. Comput. 77, No. 264, 2141--2153 (2008; Zbl 1198.65186) Full Text: DOI
Hansen, Eskil; Ostermann, Alexander Dimension splitting for evolution equations. (English) Zbl 1149.65084 Numer. Math. 108, No. 4, 557-570 (2008). Reviewer: Dinh Nho Hao (Hanoi) MSC: 65M70 35K90 65M12 PDF BibTeX XML Cite \textit{E. Hansen} and \textit{A. Ostermann}, Numer. Math. 108, No. 4, 557--570 (2008; Zbl 1149.65084) Full Text: DOI
Huhtanen, Marko Energy conservation and unitary approximation numbers. (English) Zbl 1144.81359 J. Math. Phys. 48, No. 7, 073512, 6 p. (2007). MSC: 15A18 PDF BibTeX XML Cite \textit{M. Huhtanen}, J. Math. Phys. 48, No. 7, 073512, 6 p. (2007; Zbl 1144.81359) Full Text: DOI
Papageorgiou, A. On the complexity of the multivariate Sturm-Liouville eigenvalue problem. (English) Zbl 1129.65079 J. Complexity 23, No. 4-6, 802-827 (2007). MSC: 65N25 35P15 65Y20 PDF BibTeX XML Cite \textit{A. Papageorgiou}, J. Complexity 23, No. 4--6, 802--827 (2007; Zbl 1129.65079) Full Text: DOI
Dujardin, Guillaume; Faou, Erwan Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential. (English) Zbl 1137.65062 Numer. Math. 108, No. 2, 223-262 (2007). Reviewer: Jialin Hong (Beijing) MSC: 65P10 37M15 37K55 PDF BibTeX XML Cite \textit{G. Dujardin} and \textit{E. Faou}, Numer. Math. 108, No. 2, 223--262 (2007; Zbl 1137.65062) Full Text: DOI
Le Roux, S.; Zérah, G. Convergence stability and estimator in orbital free electronic structure calculation on a grid at finite temperature. (English) Zbl 1351.82103 J. Comput. Phys. 226, No. 2, 2063-2077 (2007). MSC: 82D10 65Z05 81V10 PDF BibTeX XML Cite \textit{S. Le Roux} and \textit{G. Zérah}, J. Comput. Phys. 226, No. 2, 2063--2077 (2007; Zbl 1351.82103) Full Text: DOI
Descombes, Stéphane; Dumont, Thierry; Louvet, Violaine; Massot, Marc On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients. (English) Zbl 1122.65061 Int. J. Comput. Math. 84, No. 6, 749-765 (2007). Reviewer: Qin Mengzhao (Beijing) MSC: 65L05 65M12 65M15 65M20 34A30 35K57 PDF BibTeX XML Cite \textit{S. Descombes} et al., Int. J. Comput. Math. 84, No. 6, 749--765 (2007; Zbl 1122.65061) Full Text: DOI
Huhtanen, Marko Averaging operators for exponential splittings. (English) Zbl 1120.65051 Numer. Math. 106, No. 3, 511-528 (2007). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65F30 PDF BibTeX XML Cite \textit{M. Huhtanen}, Numer. Math. 106, No. 3, 511--528 (2007; Zbl 1120.65051) Full Text: DOI
Gradinaru, V. Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation. (English) Zbl 1117.65137 Computing 80, No. 1, 1-22 (2007). MSC: 65M70 35Q40 81Q05 65T40 81-08 65M12 PDF BibTeX XML Cite \textit{V. Gradinaru}, Computing 80, No. 1, 1--22 (2007; Zbl 1117.65137) Full Text: DOI
Dujardin, Guillaume; Faou, Erwan Long time behavior of splitting methods applied to the linear Schrödinger equation. (English) Zbl 1110.65089 C. R., Math., Acad. Sci. Paris 344, No. 2, 89-92 (2007). MSC: 65M20 35Q40 81Q05 37K10 PDF BibTeX XML Cite \textit{G. Dujardin} and \textit{E. Faou}, C. R., Math., Acad. Sci. Paris 344, No. 2, 89--92 (2007; Zbl 1110.65089) Full Text: DOI
Huhtanen, Marko; Nevanlinna, Olavi A minimum residual algorithm for solving linear systems. (English) Zbl 1102.65035 BIT 46, No. 3, 533-548 (2006). MSC: 65F10 PDF BibTeX XML Cite \textit{M. Huhtanen} and \textit{O. Nevanlinna}, BIT 46, No. 3, 533--548 (2006; Zbl 1102.65035) Full Text: DOI
Koch, Othmar; Kreuzer, Wolfgang; Scrinzi, Armin Approximation of the time-dependent electronic Schrödinger equation by MCTDHF. (English) Zbl 1088.65092 Appl. Math. Comput. 173, No. 2, 960-976 (2006). MSC: 65M70 35Q40 81Q05 65M20 PDF BibTeX XML Cite \textit{O. Koch} et al., Appl. Math. Comput. 173, No. 2, 960--976 (2006; Zbl 1088.65092) Full Text: DOI
Faugeras, Blaise; Pousin, Jérôme; Fontvieille, Franck An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system. (English) Zbl 1107.65082 Math. Comput. 75, No. 253, 209-222 (2006). Reviewer: Jialin Hong (Beijing) MSC: 65M20 35K57 65M12 80A30 PDF BibTeX XML Cite \textit{B. Faugeras} et al., Math. Comput. 75, No. 253, 209--222 (2006; Zbl 1107.65082) Full Text: DOI
Pareschi, Lorenzo; Russo, Giovanni Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. (English) Zbl 1203.65111 J. Sci. Comput. 25, No. 1-2, 129-155 (2005). MSC: 65L06 65C20 82D25 35L65 65M06 PDF BibTeX XML Cite \textit{L. Pareschi} and \textit{G. Russo}, J. Sci. Comput. 25, No. 1--2, 129--155 (2005; Zbl 1203.65111) Full Text: DOI
Kozlov, Roman; Kværnø, Anne; Owren, Brynjulf The behaviour of the local error in splitting methods applied to stiff problems. (English) Zbl 1053.65061 J. Comput. Phys. 195, No. 2, 576-593 (2004). MSC: 65L70 34A34 65L05 34A26 65L50 34E15 PDF BibTeX XML Cite \textit{R. Kozlov} et al., J. Comput. Phys. 195, No. 2, 576--593 (2004; Zbl 1053.65061) Full Text: DOI
Lubich, Christian A variational splitting integrator for quantum molecular dynamics. (English) Zbl 1037.81634 Appl. Numer. Math. 48, No. 3-4, 355-368 (2004). MSC: 81V55 81-08 PDF BibTeX XML Cite \textit{C. Lubich}, Appl. Numer. Math. 48, No. 3--4, 355--368 (2004; Zbl 1037.81634) Full Text: DOI
Descombes, Stéphane; Schatzman, Michelle Strang’s formula for holomorphic semi-groups. (English) Zbl 1030.35095 J. Math. Pures Appl., IX. Sér. 81, No. 1, 93-114 (2002). Reviewer: Michael Perelmuter (Kyïv) MSC: 35K15 47D06 35A35 PDF BibTeX XML Cite \textit{S. Descombes} and \textit{M. Schatzman}, J. Math. Pures Appl. (9) 81, No. 1, 93--114 (2002; Zbl 1030.35095) Full Text: DOI
Ostermann, Alexander Stability of W-methods with applications to operator splitting and to geometric theory. (English) Zbl 1007.65063 Appl. Numer. Math. 42, No. 1-3, 353-366 (2002). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M12 34G20 65L05 65L12 65M06 35K90 PDF BibTeX XML Cite \textit{A. Ostermann}, Appl. Numer. Math. 42, No. 1--3, 353--366 (2002; Zbl 1007.65063) Full Text: DOI