scholarly journals Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime

2020 ◽  
Vol 89 (325) ◽  
pp. 2141-2173 ◽  
Author(s):  
Weizhu Bao ◽  
Yongyong Cai ◽  
Jia Yin
Keyword(s):  
Dirac Equation ◽  
Super Resolution ◽  
Splitting Methods ◽  
Time Splitting

Time-Splitting Methods to Solve the Stochastic Incompressible Stokes Equation

2012 ◽  
Vol 50 (6) ◽  
pp. 2917-2939 ◽  
Author(s):  
Erich Carelli ◽  
Erika Hausenblas ◽  
Andreas Prohl
Keyword(s):  
Stokes Equation ◽  
Splitting Methods ◽  
Time Splitting

Efficient removal of boundary-divergence errors in time-splitting methods

1989 ◽  
Vol 4 (3) ◽  
pp. 291-308 ◽  
Author(s):  
A. G. Tomboulides ◽  
M. Israeli ◽  
G. E. Karniadakis
Keyword(s):  
Splitting Methods ◽  
Efficient Removal ◽  
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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