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Keywords

Sine-Gordon system
Finite difference methods
explicit method
Crank-Nicholson method
Stability Analysis
Fourier(Von-Neumann) method

Abstract

This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer . We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit  method is stable under the condition    and  .  
https://doi.org/10.33899/csmj.2010.163896
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