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AL-Rafidain Journal of Computer Sciences and Mathematics

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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
10.33899/csmj.2010.163896

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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  .
 
Keywords:
    Sine-Gordon system Finite difference methods explicit method Crank-Nicholson method Stability Analysis Fourier(Von-Neumann) method
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(2010). Numerical Solution for Sine-Gordon System in One Dimension. AL-Rafidain Journal of Computer Sciences and Mathematics, 7(2), 47-59. doi: 10.33899/csmj.2010.163896
Saad A. Manna; Haneen T. Jassim. "Numerical Solution for Sine-Gordon System in One Dimension". AL-Rafidain Journal of Computer Sciences and Mathematics, 7, 2, 2010, 47-59. doi: 10.33899/csmj.2010.163896
(2010). 'Numerical Solution for Sine-Gordon System in One Dimension', AL-Rafidain Journal of Computer Sciences and Mathematics, 7(2), pp. 47-59. doi: 10.33899/csmj.2010.163896
Numerical Solution for Sine-Gordon System in One Dimension. AL-Rafidain Journal of Computer Sciences and Mathematics, 2010; 7(2): 47-59. doi: 10.33899/csmj.2010.163896
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