An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

2019 ◽  
Vol 351 ◽  
pp. 124-138
Author(s):  
Jingjun Zhao ◽  
Yu Li ◽  
Yang Xu
Keyword(s):  
Nonlinear Wave ◽  
Fourth Order ◽  
Wave Equations ◽  
Riesz Space ◽  
Nonlinear Wave Equations ◽  
Order Energy

Numerical Solution of the Nonlinear Wave Equation via Fourth-Order Time Stepping

2015 ◽  
Vol 729 ◽  
pp. 213-219
Author(s):  
Mohammadreza Askaripour Lahiji ◽  
Zainal Abdul Aziz
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Fourth Order ◽  
Nonlinear Wave Equation ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Fisher Equation ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Time Stepping

Some nonlinear wave equations are more difficult to solve analytically. Exponential Time Differencing (ETD) technique requires minimum stages to obtain the required accurateness, which suggests an efficient technique relating to computational duration that ensures remarkable stability characteristics upon resolving the nonlinear wave equations. This article solves the non-diagonal example of Fisher equation via the exponential time differencing Runge-Kutta 4 method (ETDRK4). Implementation of the method is demonstrated by short Matlab programs.

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