Energy-decreasing Exponential Time Differencing Runge–Kutta methods for phase-field models

2022 ◽  
pp. 110943
Author(s):  
Zhaohui Fu ◽  
Jiang Yang
Keyword(s):  
Phase Field ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Phase Field Models ◽  
Runge Kutta

scholarly journals Convex Splitting Runge–Kutta methods for phase-field models

2017 ◽  
Vol 73 (11) ◽  
pp. 2388-2403 ◽  
Author(s):  
Jaemin Shin ◽  
Hyun Geun Lee ◽  
June-Yub Lee
Keyword(s):  
Phase Field ◽  
Phase Field Models ◽  
Convex Splitting ◽  
Runge Kutta

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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