A reliable approach to the Korteweg-de Vries equation.: An application of the decomposition method

Kybernetes

Volumn 34, Issue 7-8, 2005, Pages 951-959

  Inc, M ^a   Cherruault, Y ^b  

^a FIRAT UNIVERSITY   (Turkey)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Cybernetics; Mathematical analysis; Mathematical modelling

Indexed keywords

EID: 24344452918     PISSN: 0368492X     EISSN: None     Source Type: Journal    
DOI: 10.1108/03684920510605777     Document Type: Review

References (18)

1. Adomian, G. (1986), Non-linear Stochastic Operator Equations, Academic Press, San Diego, CA.
2. Adomian, G. (1988), "A review of the decomposition method in applied mathematics", J. Math. Anal. Appl., Vol. 135, pp. 501-44.
3. Adomian, G. (1994), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, MA.
4. Adomian, G. and Rach, R. (1992), "Noise terms in decomposition solution, series", Comput. Math. Appl., Vol. 24 No. 11, pp. 61-4.
5. Cherruault, Y. (1998a), Modéles et Méthodes Mathématiques pour les Sciences du Vivant, Presses Universitaires de France, Paris.
6. Cherruault, Y. (1998b), Optimisation, Méthodes Locales et Globales, Presses Universitaires de France, Paris.
7. Cherruault, Y., Inc, M. and Abbaoui, K. (2002), "On the solution of the non-linear KdV equation by the decomposition method", Kybernetes, Vol. 31 No. 5, pp. 766-72.
8. Inc, M. and Cherruault, Y. (2002), "A new approach to solve a diffusion-convection problem", Kybernetes, Vol. 31 Nos 3/4, pp. 536-49.
9. Kaya, D. (2000), "An application of the decomposition method for second-order wave equations", Intern. J. Comput. Math., Vol. 75, pp. 235-45.
10. Kaya, D. (2001a), "An explicit solution of coupled viscous Burgers' equation by the decomposition method", Int. J. Math. Math. Sci, 27 11 pp. 675-80.
11. Kaya, D. (2001b), "Explicit solutions of generalized non-linear Boussinesq equations", J. Appl. Math., Vol. 1 No. 1, pp. 29-37.
12. Mavoungou, T. and Cherruault, Y. (1992), "Convergence of Adomian method and applications to non-linear PDEs", Kybernetes, Vol. 21 No. 6, pp. 13-25.
13. Mavoungou, T. and Cherruault, Y. (1994), "Numerical study of Fisher's equation by Adomian's method", Math. Comput Modelling, Vol. 19 No. 1, pp. 89-95.
14. Ngarhasta, N., Some, B., Abbaoui, K. and Cherruault, Y. (2002), "New numerical study of Adomian method applied to a diffusion model", Kybernetes, Vol. 31 No. 1, pp. 61-75.
15. Wazwaz, A.M. (1995a), "A new approach to the non-linear advection problem: an application of the decomposition method", Applied Math. Comput., Vol. 72, pp. 175-81.
16. Wazwaz, A.M. (1995b), "The decomposition method for approximate solution of the Goursat problem", Appl. Math. Comput., Vol. 69, pp. 299-311.
17. Wazwaz, A.M. (1997), "Necessary conditions for the appearance of noise terms in decomposition solution series", Appl. Math. Comput., Vol. 5, pp. 265-74.
18. Whitham, G.B. (1974), Linear and Non-linear Waves, Wiley, San Diego, CA.