Error estimates of a conservative finite difference Fourier pseudospectral method for the Klein–Gordon–Schrödinger equation

2020 ◽  
Vol 79 (7) ◽  
pp. 1956-1971 ◽  
Author(s):  
Bingquan Ji ◽  
Luming Zhang
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Error Estimates ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Fourier Pseudospectral Method ◽  
Klein Gordon ◽  
Fourier Pseudospectral ◽  
Difference Fourier

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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