Numerical Solution and Stability Analysis of the Sine-Gordon Equation
AL-Rafidain Journal of Computer Sciences and Mathematics,
2007, Volume 4, Issue 1, Pages 39-56
AbstractThe 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 .
- Article View: 72
- PDF Download: 104