Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
SIAM Journal on Numerical Analysis
The Reduced Basis Element Method: Application to a Thermal Fin Problem
SIAM Journal on Scientific Computing
Introduction to Data Compression, Third Edition (Morgan Kaufmann Series in Multimedia Information and Systems)
Quantum Control With Piecewise Constant Control Functions
SIAM Journal on Scientific Computing
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The goal of this paper is to provide an analysis of the "toolkit" method used in the numerical approximation of the time-dependent Schrödinger equation. The "toolkit" method is based on precomputation of elementary propagators and was seen to be very efficient in the optimal control framework. Our analysis shows that this method provides better results than the second order Strang operator splitting. In addition, we present two improvements of the method in the limit of low and large intensity control fields.