Keywords : Sine-Gordon system


Numerical solution and stability analysis of the Sine-Gordon system in two dimensions

Saad A. Manna; Haneen T. Jassim

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 1, Pages 13-25
DOI: 10.33899/csmj.2012.163684

This paper deals with the numerical solution for Sine-Gordon system in two dimensions using two finite difference methods the (ADE) and (ADI) methods .A comparison between the two methods has been done and we have obtained that the (ADE) method is the easer while the (ADI) method is more accurate than the (ADE) method. We also studied the stability analysis for each method by using Fourier (Von Neumann) method and we have obtained that the (ADI) method is unconditionally stable while the (ADE) method is stable under the condition  and    where  is the ratio of the waves speed  u , w and . 
 
 

Numerical Solution for Sine-Gordon System in One Dimension

Saad A. Manna; Haneen T. Jassim

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 2, Pages 47-59
DOI: 10.33899/csmj.2010.163896

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  .