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Keywords

Stability Analysis
Finite Differences Methods
Explicit Scheme
Crank – Nicholson method
Fourier (Von Neumann) method
Sine-Gordon Equation

Abstract

The Sine – Gordon equation has been solved numerically by using two finite differences methods: The first is the explicit scheme and the second is the Crank – Nicholson scheme. A comparison between the two schemes has been made and the results were found to be : the first scheme is simpler and has faster convergence while the second scheme is more accurate . Also , the stability analysis of the two methods by the use of Fourier (Von Neumann) method has been done and the results were found to be : The explicit scheme is conditionally stable if  and the Crank–Nicholson is unconditionally stable .  
https://doi.org/10.33899/csmj.2007.164002
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