On the asymptotic behavior of high order moments for a family of Schrödinger equations

2021 ◽  
Vol 78 (1) ◽  
pp. 101-128
Author(s):  
Nikolay Tzvetkov ◽  
Nicola Visciglia
Keyword(s):  
Asymptotic Behavior ◽  
High Order ◽  
Schrodinger Equations ◽  
Schrödinger Equations

Asymptotic behavior of cubic defocusing Schrödinger equations on compact surfaces

2018 ◽  
Vol 69 (4) ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Wellington J. Corrêa ◽  
Valéria N. Domingos Cavalcanti ◽  
Maria R. Astudillo Rojas
Keyword(s):  
Asymptotic Behavior ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Compact Surfaces

The Conservative Splitting High-Order Compact Finite Difference Scheme for Two-Dimensional Schrödinger Equations

2017 ◽  
Vol 15 (01) ◽  
pp. 1750079
Author(s):  
Bo Wang ◽  
Dong Liang ◽  
Tongjun Sun
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Two Dimensions ◽  
High Order ◽  
Optimal Error Estimate ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Dimensional ◽  
Time Step ◽  
Order Accuracy

In this paper, a new conservative and splitting fourth-order compact difference scheme is proposed and analyzed for solving two-dimensional linear Schrödinger equations. The proposed splitting high-order compact scheme in two dimensions has the excellent property that it preserves the conservations of charge and energy. We strictly prove that the scheme satisfies the charge and energy conservations and it is unconditionally stable. We also prove the optimal error estimate of fourth-order accuracy in spatial step and second-order accuracy in time step. The scheme can be easily implemented and extended to higher dimensional problems. Numerical examples are presented to confirm our theoretical results.

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