Paper Info
Title
Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations.
Abstract
In this work, the error behavior of operator splitting methods is analyzed for highly-oscillatory differential equations. The scope of applications includes time-dependent nonlinear Schrodinger equations, where the evolution operator associated with the principal linear part is highly-oscillatory and periodic in time. In a first step, a known convergence result for the second-order Strang splitting method applied to the cubic Schrodinger equation is adapted to a wider class of nonlinearities. In a second step, the dependence of the global error on the decisive parameter 0 < epsilon << 1, defining the length of the period, is examined. The main result states that, compared to established error estimates, the Strang splitting method is more accurate by a factor e, provided that the time stepsize is chosen as an integer fraction of the period. This improved error behavior over a time interval of fixed length, which is independent of the period, is due to an averaging effect. The extension of the convergence result to higher-order splitting methods and numerical illustrations complement the investigations.
Year
DOI
Venue
2016
10.1090/mcom/3088
MATHEMATICS OF COMPUTATION
Keywords
Field
DocType
Highly-oscillatory differential equations,time-dependent nonlinear Schrodinger equations,operator splitting methods,Strang splitting method,error estimate,convergence result,averaging
Integer,Convergence (routing),Strang splitting,Differential equation,Mathematical optimization,Nonlinear system,Mathematical analysis,Schrödinger equation,Operator (computer programming),Periodic graph (geometry),Mathematics
Journal
Volume
Issue
ISSN
85
302
0025-5718
Citations 
PageRank 
References 
3
0.39
2
Authors
4
Name
Order
Citations
PageRank
P. Chartier114429.70
Florian Méhats28014.01
Mechthild Thalhammer312416.02
Yong Zhang4294.56