Runge-kutta Exponential Time Differencing Method Analysis of Non-magnetized Plasma Stealth

2010 ◽  
Vol 31 (9) ◽  
pp. 1075-1080 ◽  
Author(s):  
Hong Wei Yang ◽  
Yan Liu
Keyword(s):  
Magnetized Plasma ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Runge Kutta ◽  
Exponential Time Differencing Method ◽  
Method Analysis

scholarly journals Fourier Spectral Method for a Class of Nonlinear Schrödinger Models

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Lei Zhang ◽  
Weihua Ou Yang ◽  
Xuan Liu ◽  
Haidong Qu
Keyword(s):  
Spectral Method ◽  
Fourth Order ◽  
Fourier Spectral Method ◽  
Spatial Direction ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Nonlinear Schrödinger ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Temporal Direction

In this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential time-differencing Runge-Kutta method is used to discrete temporal direction. The proof of the conservation law of the mass and the energy for the semidiscrete and full-discrete Fourier spectral scheme is given. The error of the semidiscrete Fourier spectral scheme is analyzed in the proper Sobolev space. Finally, several numerical examples are presented to support our analysis.

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