TY - JOUR
T1 - On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations
AU - Ranocha, Hendrik
AU - Quezada de Luna, Manuel
AU - Ketcheson, David I.
N1 - KAUST Repository Item: Exported on 2021-11-22
Acknowledgements: Open Access funding enabled and organized by Projekt DEAL.
PY - 2021/10/18
Y1 - 2021/10/18
N2 - AbstractWe study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.
AB - AbstractWe study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.
UR - http://hdl.handle.net/10754/673702
UR - https://link.springer.com/10.1007/s42985-021-00126-3
U2 - 10.1007/s42985-021-00126-3
DO - 10.1007/s42985-021-00126-3
M3 - Article
SN - 2662-2963
VL - 2
JO - Partial Differential Equations and Applications
JF - Partial Differential Equations and Applications
IS - 6
ER -