On the solutions of the time-delayed Burgers equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 12, 2008, Pages 4775-4786

  Fahmy, E S ^a   Abdusalam, H A ^b   Raslan, K R ^c  

^a KING SAUD UNIVERSITY   (Saudi Arabia)

^b CAIRO UNIVERSITY   (Egypt)

^c AL AZHAR UNIVERSITY   (Egypt)

Author keywords

Adomian decomposition method; Tanh function method; Time delayed Burgers equation; Travelling wave; Variational iteration method

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; OPERATIONS RESEARCH; OSCILLATORS (MECHANICAL); PARTICLE SIZE ANALYSIS; PROBABILITY DENSITY FUNCTION; TURBULENCE;

ADOMIAN DECOMPOSITION METHOD; TANH-FUNCTION METHOD; TIME-DELAYED BURGERS EQUATION; TRAVELLING WAVE; VARIATIONAL ITERATION METHOD;

ITERATIVE METHODS;

EID: 55049093741     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.11.027     Document Type: Article

References (27)

1. Debnath L. Nonlinear Partial Differential Equations for Sciences and Engineers (1997), Birkhauser, Boston
2. Wilmott P., Howison S., and Dewynne J. The Mathematics of Financial Derivatives (2002), Cambridge Univ. Press
3. Okubo A. Diffusion and Ecological Problems: Mathematical Models (1980), Springer-Verlag
4. Murray J.D. Mathematical Biology I. An introduction. third ed. (2003), Springer-Verlag, Berlin, Heidelberg
5. Burgers J.M. Adv. Appl. Mech. 1 (1948) 171
6. Kar S., Banik S.K., and Ray D.S. Exact solutions of Fisher and Burgers equations with finite transport memory. Journal of Physics. A. Mathematical and General 36 (2003) 2771
7. Abdusalam H.A. Exact analytic solution of the simplified telegraph model of propagation and dissipation of exciton fronts. International Journal of Theoretical Physics 43 4 (2004) 1161
8. Ahmed E., and Abdusalam H.A. On modified Black-Scholes equation. Chaos, Solitons and Fractals 22 3 (2004) 583
9. Parkes E.J., and Duffy B.R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Computer Physics Communications 98 3 (1996) 288
10. Li Z.B., and Liu Y.P. RATH: A maple package for finding travelling solitary wave solutions to nonlinear evolution equations. Computer Physics Communications 148 2 (2002) 256
11. Fan E.G. Extended tanh-function method and its applications to nonlinear equations. Physical Letters A 277 (2000) 212
12. Wazwaz A.M. The tanh-method: Solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos, Solitons and Fractals 25 (2005) 55
13. Evans D.J., and Raslan K.R. Tanh method for nonlinear partial differential equations. International Journal of Computer Mathematics, (UK) 82 7 (2005) 897-905
14. Fu Z.T., Liu S.K., Liu S.D., and Zhao Q. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physical Letters A 290 (2001) 72
15. Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons and Fractals 24 (2005) 1217
16. Vladimirov V.A., and Kutafina E.V. Exact travelling wave solutions of some nonlinear evolutionary equations. Reports on Mathematical Physics 54 (2004) 261
17. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic, Boston, MA
18. Bobolian E., and Javadi S. New method for calculating Adomian polynomials. Applied Mathematics and Computation 153 (2004) 253
19. Raslan K.R. The decomposition method for a Hirota-Satsuma coupled MKDV equation. International Journal of Computer Mathematics 81 12 (2004) 1497
20. Evans D.J., and Raslan K.R. The Adomian decomposition method for solving delay differential equation. International Journal of Computer Mathematics 82 1 (2005) 49
21. He J.H. Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation 114 (2000) 115
22. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 65
23. Sweilam N.H., and Khader M.M. Variational iteration method for one dimensional nonlinear thermoelectricity. Chaos, Solitons and Fractals 32 (2007) 145
24. Wazwaz A.M. A comparison between the variational iteration method and Adomian decomposition method. Journal of Computational and Applied Mathematics 207 (2007) 129-136
25. Soliman A.A., and Abdou M.A. Numerical solutions of nonlinear evolution equations using variational iteration method. Journal of Computational and Applied Mathematics 207 (2007) 111-120
26. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burgers' and coupled Burgers' equation. Journal of Computational and Applied Mathematics 181 (2005) 245
27. Abdusalam H.A. Multiple soliton solutions for the Nagumo equation and the modified general Burgers-Fisher equation. International Journal of Computational Methods 3 3 (2006) 371