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International Journal of Computer Mathematics Volume 83, 2006 - Issue 3
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Original Articles

Petrov–Galerkin method and K(2, 2) equation

D. S. Mashat Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
,
L. A. Wazzan Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
&
M. S. Ismail Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi ArabiaCorrespondence[email protected]
Pages 331-343 | Received 19 Aug 2005, Accepted 06 Apr 2006, Published online: 17 Feb 2007

References

  • Bullough , R. K. and Caudrey , P. J. 1980 . Solitons , Berlin : Springer-Verlag .
  • Chertock , A. and Levy , D. 2001 . Particle methods for dispersive equations . Journal of Computational Physics , 171 : 708 – 730 .
  • Christie , I. , Griffiths , D. , Mitchell , A. and Sanz-Serna , J. M. 1981 . Product approximation for non-linear problems in the finite element method . IMA Journal of Numerical Analysis , 1 : 253 – 266 .
  • Frutsos , J. , Marcos , A. L. and Sanz-Serna , J. M. 1995 . A finite difference scheme for the K(2, 2) equation . Journal of Computational Physics , 120 : 248 – 252 .
  • Ismail , M. S. and Taha , T. R. A numerical study of Korteweg–de Vries-like equations . August 24–29 1997 , Berlin , Germany. Proceedings of the 15th Imacs World Congress on Scientific Computation Modelling and Applied Mathematics , Edited by: Sydow , A. Vol. 2 , pp. 131 – 136 . Berlin : Wissenschaft & Technik Verlag .
  • Ismail , M. S. and Taha , T. R. 1998 . A numerical study of compactons . Mathematics and Computing in Simulation , 47 : 519 – 530 .
  • Ismail , M. S. 2000 . A finite difference method of Korteweg–de Vries-like equation with nonlinear dispersion . International Journal of Computer Mathematics , 74 : 158 – 193 .
  • Ismail , M. S. and Al-Solamy , F. R. 2001 . A numerical study of K (3,2) equations . International Journal of Computer Mathematics , 76 : 549 – 560 .
  • Remoissenet , M. 1996 . Waves called Solitons: Concepts and experiments , Berlin : Springer-Verlag .
  • Wadati , M. 2001 . Introduction to solitons . Pramana–Journal of Physics , 57 : 841 – 847 .
  • Rosenau , P. and Hyman , J. M. 1993 . Compacton solitons with finite lengths . Physical Review Letters , 70 : 564 – 567 .
  • Wazwaz , A. M. 2002 . New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations . Chaos, Solitons and Fractals , 13 : 321 – 330 .
  • Wazwaz , A. M. 2004 . The sine–cosine method for obtaining solutions with compact and noncompact structures . Applied Mathematics and Computing , 159 : 559 – 576 .
  • Taha , T. R. and Schiesser , W. E. Method of lines solution of the K(2,2) Compacton (KdV-type) equation . August 24–29 1997 , Berlin , Germany. Proceedings of the 15th Imacs World Congress on Scientific Computation, Modelling and Applied Mathematics , Edited by: Sydow , A. Vol. 2 , pp. 127 – 130 . Berlin : Wissenschaft & Technik Verlag .
  • Sanz-Serna , J. M. and Christie , I. 1981 . Petrov–Galerkin methods for nonlinear dispersive waves . Journal of Computational Physics , 39 : 94 – 103 .
  • Thomas , J. W. 1985 . Numerical Partial Differential Equations , Vol. 22 , Berlin : Springer-Verlag . Texts in Applied Math

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