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Nonlinear eigenvalue problems with symmetry

Author

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  • Syam, Muhammed I.
  • Khashan, Hani A.
  • Al-Mdallal, Qasem M.

Abstract

In this paper we use the conjugate gradient predictor corrector method (CGPCM) in the context of continuation methods. By exploiting symmetry in certain nonlinear eigenvalue problems, we can decompose the centered difference discretization matrices into small ones and reduce computational cost. We use the cyclic group of order two to divide the system into two smaller systems. We reduce the cost and the computational time by combining CGPCM with the idea of the exploiting symmetries. Theoretical and numerical results are presented. Conclusions are given.

Suggested Citation

  • Syam, Muhammed I. & Khashan, Hani A. & Al-Mdallal, Qasem M., 2008. "Nonlinear eigenvalue problems with symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 931-941.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:5:p:931-941
    DOI: 10.1016/j.chaos.2006.05.083
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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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    Cited by:

    1. Ye, Wang-Chuan & Li, Biao, 2009. "Finite symmetry transformation groups and exact solutions of the cylindrical Korteweg-de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2623-2628.

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