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Original Articles

On the exact and numerical solution of the time-delayed Burgers equation

, &
Pages 1637-1648 | Received 17 Jan 2006, Accepted 24 Jun 2007, Published online: 09 Oct 2008

References

  • Abdusalam , H. A. 2004 . Exact analytic solution of the simplified telegraph model of propagation and dissipation of excition fronts . Int. J. Theoret. Phys. , 43 ( 4 ) : 1161
  • Adomian , G. 1994 . Solving Frontier Problems of Physics: The Decomposition Method , Boston, MA : Kluwer Academic .
  • Ahmed , E. and Abdusalam , H. A. 2004 . On modified Black-Scholes equation . Chaos Solitons Fractals. , 22 ( 3 ) : 583
  • Bobolian , E. and Javadi , S. 2004 . New method for calculating Adomian polynomials . Appl. Math. Comput. , 153 : 253
  • Burgers , J. M. 1948 . A mathematical model illustrating the theory of turbulence . Adv. Appl. Mech. , 1 : 171
  • Debnath , L. 1997 . “ Nonlinear Partial Differential Equations for Sciences and Engineers ” . In Birkhauser Boston
  • Evans , D. J. and Raslan , K. R. 2005 . The Adomian decomposition method for solving delay differential equation . Int. J. Comput. Math. , 82 ( 1 ) : 49
  • Evans , D. J. and Raslan , K. R. 2005 . The tanh-function method for solving some important nonlinear partial differential equations . Int. J. Comput. Math. , 82 ( 7 ) : 876
  • Fahmy , E. S. 2007 . Exact solution of the generalized time-delayed Burgers equation through the improved tanh-function method . J. Math. Control Sci. Appl. , 1 ( 1 ) : 63
  • Fan , E. G. 2000 . Extended tanh-function method and its applications to nonlinear equations . Phys. Lett. A. , 277 : 212
  • Fu , Z. T. , Liu , S. K. , Liu , S. D. and Zhao , Q. 2001 . New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations . Phys. Lett. A. , 290 : 72
  • Kudryashov , N. A. 2005 . Simplist equation method to look for exact solutions of nonlinear differential equations . Chaos, Solitons Fractals. , 24 : 1217
  • Li , Z. B. and Liu , Y. P. 2002 . RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations . Comput. Phys. Commun. , 148 ( 2 ) : 256
  • Murray , J. D. 2003 . Mathematical Biology I. An introduction , 3 , Berlin Heidelberg : Springer-Verlag .
  • Okubo , A. 1980 . “ Diffusion and ecological problems: Mathematical Models ” . Springer – Verlag .
  • Parkes , E. J. and Duffy , B. R. 1996 . An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations . Comput. Phys. Commun. , 98 ( 3 ) : 288
  • Raslan , K. R. 2004 . The decomposition method for a Hirota-Satsuma coupled MKDV equation . Int. J. Comput. Math. , 81 ( 12 ) : 1497
  • Vladimirov , V. A. and Kutafina , E. V. 2004 . Exact travelling wave solutions of some nonlinear evolutionary equations . Reports Math. Phys. , 54 : 261
  • Wazwaz , A. M. 2005 . The tanh-method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations . Chaos, Solitons Fractals. , 25 : 55
  • Wilmott , P. , Howison , S. and Dewynne , J. 2002 . The Mathematics of Financial Derivatives , Cambridge Univ. Press .

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