We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.
Accepté le :
DOI : 10.1051/m2an/2019033
Keywords: Multi-configuration time-dependent Hartree–Fock method, exponential Lawson multistep methods, stability, local error, convergence
Koch, Othmar 1
@article{M2AN_2019__53_6_2109_0,
author = {Koch, Othmar},
title = {Convergence of exponential {Lawson-multistep} methods for the {MCTDHF} equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2109--2119},
year = {2019},
publisher = {EDP Sciences},
volume = {53},
number = {6},
doi = {10.1051/m2an/2019033},
mrnumber = {4041518},
zbl = {1431.65148},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2019033/}
}
TY - JOUR AU - Koch, Othmar TI - Convergence of exponential Lawson-multistep methods for the MCTDHF equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2019 SP - 2109 EP - 2119 VL - 53 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2019033/ DO - 10.1051/m2an/2019033 LA - en ID - M2AN_2019__53_6_2109_0 ER -
%0 Journal Article %A Koch, Othmar %T Convergence of exponential Lawson-multistep methods for the MCTDHF equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2019 %P 2109-2119 %V 53 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2019033/ %R 10.1051/m2an/2019033 %G en %F M2AN_2019__53_6_2109_0
Koch, Othmar. Convergence of exponential Lawson-multistep methods for the MCTDHF equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 2109-2119. doi: 10.1051/m2an/2019033
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