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Efficient adaptive exponential time integrators for nonlinear Schrödinger equations with nonlocal potential
Winfried Auzinger, Iva Březinová, Alexander Grosz, Harald Hofstätter, Othmar Koch and Takeshi Sato Journal of Computational Mathematics and Data Science 1 100014 (2021) https://doi.org/10.1016/j.jcmds.2021.100014
Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs
A Quantum Model for the Dynamics of Cold Dark Matter
Tim Zimmermann, Massimo Pietroni, Javier Madroñero, Luca Amendola and Sandro Wimberger Condensed Matter 4(4) 89 (2019) https://doi.org/10.3390/condmat4040089
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 Quell Computer Physics Communications 234 55 (2019) https://doi.org/10.1016/j.cpc.2018.08.003
Strang Splitting in Combination with Rank-1 and Rank-r Lattices for the Time-Dependent Schrödinger Equation
Yuya Suzuki, Gowri Suryanarayana and Dirk Nuyens SIAM 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
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 Thalhammer Journal of Computational and Applied Mathematics 273 182 (2015) https://doi.org/10.1016/j.cam.2014.06.012
Convergence analysis of high-order time-splitting pseudo-spectral methods for rotational Gross–Pitaevskii equations