Numerical Solution and Stability Analysis of the Sine-Gordon Equation

• Main Authors: Saad Manna, Norjan Juma
• Format: Article
• Language: Arabic
• Published: Mosul University 2007-07-01
• Series: Al-Rafidain Journal of Computer Sciences and Mathematics
• Subjects: stability analysis; finite differences methods; explicit scheme; crank – nicholson method; fourier (von neumann) method; sine-gordon equation
• Online Access: https://csmj.mosuljournals.com/article_164002_4f2763aa77b4c29810dcede770b819b8.pdf

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 .