Error analysis of high-order splitting methods for nonlinear evolutionary Schrödinger equations and application to the MCTDHF equations in electron dynamics
ESAIM: M2AN, 47 5 (2013) 1265-1286
Published online: 2013-07-09
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Numerical Integration of Schrödinger Maps via the Hasimoto Transform
Valeria Banica, Georg Maierhofer and Katharina SchratzSIAM Journal on Numerical Analysis 62 (1) 322 (2024)
https://doi.org/10.1137/22M1531555
Convergence Analysis of the Strang Splitting Method for the Degasperis-Procesi Equation
Runjie Zhang and Jinwei FangAxioms 12 (10) 946 (2023)
https://doi.org/10.3390/axioms12100946
Canonical Euler splitting method for parabolic partial functional differential algebraic equations
Hongliang Liu, Yilin You, Haodong Li and Shoufu LiApplied Numerical Mathematics 190 65 (2023)
https://doi.org/10.1016/j.apnum.2023.04.010
Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs
Alec Dektor, Abram Rodgers and Daniele VenturiJournal of Scientific Computing 88 (2) (2021)
https://doi.org/10.1007/s10915-021-01539-3
Efficient adaptive exponential time integrators for nonlinear Schrödinger equations with nonlocal potential
Winfried Auzinger, Iva Březinová, Alexander Grosz, et al.Journal of Computational Mathematics and Data Science 1 100014 (2021)
https://doi.org/10.1016/j.jcmds.2021.100014
Colloquium : Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
Axel U. J. Lode, Camille Lévêque, Lars Bojer Madsen, Alexej I. Streltsov and Ofir E. AlonReviews of Modern Physics 92 (1) (2020)
https://doi.org/10.1103/RevModPhys.92.011001
A new high-order compact finite difference scheme based on precise integration method for the numerical simulation of parabolic equations
Changkai Chen, Xiaohua Zhang, Zhang Liu and Yage ZhangAdvances in Difference Equations 2020 (1) (2020)
https://doi.org/10.1186/s13662-019-2484-7
Large-Scale Scientific Computing
Winfried Auzinger, Alexander Grosz, Harald Hofstätter and Othmar KochLecture Notes in Computer Science, Large-Scale Scientific Computing 11958 557 (2020)
https://doi.org/10.1007/978-3-030-41032-2_64
Convergence of exponential Lawson-multistep methods for the MCTDHF equations
Othmar KochESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 2109 (2019)
https://doi.org/10.1051/m2an/2019033
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations
Winfried Auzinger, Iva Březinová, Harald Hofstätter, Othmar Koch and Michael QuellComputer Physics Communications 234 55 (2019)
https://doi.org/10.1016/j.cpc.2018.08.003
A Quantum Model for the Dynamics of Cold Dark Matter
Tim Zimmermann, Massimo Pietroni, Javier Madroñero, Luca Amendola and Sandro WimbergerCondensed Matter 4 (4) 89 (2019)
https://doi.org/10.3390/condmat4040089
Strang Splitting in Combination with Rank-1 and Rank-r Lattices for the Time-Dependent Schrödinger Equation
Yuya Suzuki, Gowri Suryanarayana and Dirk NuyensSIAM Journal on Scientific Computing 41 (6) B1254 (2019)
https://doi.org/10.1137/18M1207879
The analysis of operator splitting methods for the Camassa–Holm equation
Rui Zhan and Jingjun ZhaoApplied Numerical Mathematics 130 1 (2018)
https://doi.org/10.1016/j.apnum.2018.03.012
Convergence of a Strang splitting finite element discretization for the Schrödinger–Poisson equation
Winfried Auzinger, Thomas Kassebacher, Othmar Koch and Mechthild ThalhammerESAIM: Mathematical Modelling and Numerical Analysis 51 (4) 1245 (2017)
https://doi.org/10.1051/m2an/2016059
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
Winfried Auzinger, Othmar Koch and Michael QuellNumerical Algorithms 75 (1) 261 (2017)
https://doi.org/10.1007/s11075-016-0206-8
Strang splitting for a semilinear Schrödinger equation with damping and forcing
Tobias Jahnke, Marcel Mikl and Roland SchnaubeltJournal of Mathematical Analysis and Applications 455 (2) 1051 (2017)
https://doi.org/10.1016/j.jmaa.2017.06.004
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
Winfried Auzinger, Thomas Kassebacher, Othmar Koch and Mechthild ThalhammerNumerical Algorithms 72 (1) 1 (2016)
https://doi.org/10.1007/s11075-015-0032-4
Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method
Erik Lötstedt, Tsuyoshi Kato and Kaoru YamanouchiThe Journal of Chemical Physics 144 (15) (2016)
https://doi.org/10.1063/1.4947018
Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III: The nonlinear case
Winfried Auzinger, Harald Hofstätter, Othmar Koch and Mechthild ThalhammerJournal of Computational and Applied Mathematics 273 182 (2015)
https://doi.org/10.1016/j.cam.2014.06.012
Stiff convergence of force-gradient operator splitting methods
Emil KieriApplied Numerical Mathematics 94 33 (2015)
https://doi.org/10.1016/j.apnum.2015.03.005
Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross–Pitaevskii equations
Harald Hofstätter, Othmar Koch and Mechthild ThalhammerNumerische Mathematik 127 (2) 315 (2014)
https://doi.org/10.1007/s00211-013-0586-9
Embedded exponential operator splitting methods for the time integration of nonlinear evolution equations
O. Koch, Ch. Neuhauser and M. ThalhammerApplied Numerical Mathematics 63 14 (2013)
https://doi.org/10.1016/j.apnum.2012.09.002