An exponential wave integrator Fourier pseudospectral method for the nonlinear Schrödinger equation with wave operator

2017 ◽  
Vol 58 (1-2) ◽  
pp. 273-288 ◽  
Author(s):  
Bingquan Ji ◽  
Luming Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Nonlinear Schrodinger Equation ◽  
Fourier Pseudospectral Method ◽  
Nonlinear Schrödinger ◽  
Exponential Wave Integrator ◽  
Fourier Pseudospectral

scholarly journals Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Lv Zhong-Quan ◽  
Gong Yue-Zheng ◽  
Wang Yu-Shun
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Field Method ◽  
Nonlinear Schrodinger Equation ◽  
Fourier Pseudospectral Method ◽  
Nonlinear Schrödinger ◽  
Vector Field Method ◽  
Energy Conservation Law

Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discreteL2norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.

scholarly journals Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Langyang Huang ◽  
Zhaowei Tian ◽  
Yaoxiong Cai
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Convergence Rates ◽  
Nonlinear Schrodinger Equation ◽  
Local Conservation ◽  
Structure Preserving ◽  
Nonlinear Schrödinger ◽  
Local Momentum

Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are Oh4+τ2. The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.

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