CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 1994, Vol. 11 ›› Issue (2): 161-166.

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THE SPECTRAL METHOD FOR A PERTURBED SINE-GORDON EQUATION

Guo Boling1, Wu Xianghui2   

  1. 1. Institute of Applied physics and Computational Methematics, BeiJing 100088;
    2. Zhongshan University, Guangzhou 510275
  • Received:1992-07-15 Revised:1993-08-24 Online:1994-06-25 Published:1994-06-25

Abstract: A pertured sine-Gordon equation utt-uxx+αsinu-βuxxt=g(u),t>0,-∞< x< ∞,with the periodic initial and boundary value problem is studied. A spectral method is proposed,a priori estimates are established and the existnce and uniqueness are proved for the generalized solution.The error estimates are given and the convergence is proved for the approximate solution of the spectral method.

Key words: A pertured sine-Gordon equation, the spectral method, The convergence

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