scholarly journals An improved semi-Lagrangian time splitting spectral method for the semi-classical Schrödinger equation with vector potentials using NUFFT

2017 ◽  
Vol 111 ◽  
pp. 144-159 ◽  
Author(s):  
Zheng Ma ◽  
Yong Zhang ◽  
Zhennan Zhou
Keyword(s):  
Schrödinger Equation ◽  
Spectral Method ◽  
Schrodinger Equation ◽  
Vector Potentials ◽  
Time Splitting

scholarly journals Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation

2019 ◽  
Vol 53 (2) ◽  
pp. 443-473 ◽  
Author(s):  
Philippe Chartier ◽  
Loïc Le Treust ◽  
Florian Méhats
Keyword(s):  
Numerical Methods ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Semiclassical Limit ◽  
Splitting Methods ◽  
Convergence Behavior ◽  
First Order ◽  
Time Splitting ◽  
Uniform Accuracy

This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schrödinger equation in the semiclassical limit. We specifically analyse the convergence behavior of the first-order splitting. Our main result is a proof of uniform accuracy. We illustrate the properties of our methods with simulations.

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