scholarly journals Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator

2014 ◽  
Vol 52 (3) ◽  
pp. 1103-1127 ◽  
Author(s):  
Weizhu Bao ◽  
Yongyong Cai
Keyword(s):  
Schrödinger Equation ◽  
Error Estimates ◽  
Nonlinear Schrödinger Equation ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Nonlinear Schrodinger Equation ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Exponential Wave Integrator

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.

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