Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator

Authors:
Weizhu Bao;Yongyong Cai
Affiliations:
-;caiyongyong@nus.edu.sg
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

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Abstract

We establish uniform error estimates of finite difference methods for the nonlinear Schrödinger equation (NLS) perturbed by the wave operator (NLSW) with a perturbation strength described by a dimensionless parameter $\varepsilon$ ($\varepsilon\in(0,1]$). When $\varepsilon\to0^+$, NLSW collapses to the standard NLS. In the small perturbation parameter regime, i.e., $0