A new formulation of Adomian method: Convergence result

Kybernetes

Volumn 30, Issue 9-10, 2001, Pages 1183-1191

  Abbaoui, K ^a,b   Pujol, M J ^c   Cherruault, Y ^b   Himoun, N ^c   Grimalt, P ^d  

^a FERHAT ABBAS UNIVERSITY   (Algeria)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITÉ MOULOUD MAMMERI   (Algeria)

^d UNIVERSITY OF ALICANTE   (Spain)

Author keywords

Convergence; Cybernetics; Non linearity

Indexed keywords

ADOMIAN; ADOMIAN METHOD; CONVERGENCE; CONVERGENCE RESULTS; DECOMPOSITION METHODS; DECOMPOSITION SERIES; NEW APPROACHES; NON-LINEARITY;

CYBERNETICS;

EID: 0035732641     PISSN: 0368492X     EISSN: None     Source Type: Journal    
DOI: 10.1108/EUM0000000006549     Document Type: Article

References (16)

1. Abbaoui, K. (1995), "Les fondements mathématiques de la méthode décompositionnelle d'Adomian et application à la résolution des équations issues de la Biologie et de la Médecine", Thèse de Doctorat de l'Université de Paris VI.
2. Abbaoui, K. and Cherruault, Y. (1994a), "Convergence of the Adomian method applied to nonlinear equations", Mathematical and Computer Modelling, Vol. 20 No. 9, pp. 60-73.
3. Abbaoui, K. and Cherruault, Y. (1994b), "Convergence of Adomian method applied to differential equations", Mathematical and Computer Modelling, Vol. 28 No. 5, pp. 103-9.
4. Abbaoui, K., Cherruault, Y. and Seng, V. (1995), "Practical formulae for the calculus of multivariable Adomian polynomials", Mathematical and Computer Modelling, Vol. 22 No. 1, pp. 89-93.
5. Berge, C. (1988), Principes de Combinatoire, Dunod, Paris.
6. Cherruault, Y. (1989), "Convergence of Adomian method", Kybernetes, Vol. 18 No. 2, pp. 31-8.
7. Cherruault, Y. (1998), Modèles et méthodes mathématiques pour les sciences du vivant, Presses Universitaires de France, Paris.
8. Cherruault, Y. (1999), Optimisation. Méthodes locales et globales, Presses Universitaires de France, Paris.
9. Cherruault, Y. and Adomian, G. (1993), "Decomposition method: a new proof of convergence", Mathematical and Computer Modelling, Vol. 18 No. 12, pp. 103-6.
10. Cherruault, Y., Adomian, G., Abbaoui, K. and Rach, R. (1995), "Further remarks on convergence of decomposition method', IJBC, Vol. 38, pp. 89-93.
11. Grimalt, P. and Pujol, M.J. (1999), "The decomposition method applied to chemistry kinetics", Journal International Información Tecnológica, Vol. 10 No. 3, pp. 129-32.
12. Guellal, S., Grimalt, P. and Cherruault, Y. (1997), "Numerical study of Lorenz equations by Adomian method", Computers Math Appl., Vol. 33 No. 3, pp. 25-9.
13. Guellal, S. and Cherruault, Y. (1994), "Practical formulae for calculation of Adomian polynomials and application to the convergence of the decomposition method", IJBC, Vol. 36, pp. 223-8.
14. Guellal, S., Cherruault, Y., Pujol, M.J. and Grimalt, P. (2000), "Decomposition method applied to hydrology", Kybernetes, Vol. 29 No. 4.
15. Himoun, N., Abbaoui, K. and Cherruault, Y. (1999), "New results of convergence of Adomian method", Kybernetes, Vol. 28 Nos 4-5, pp. 423-9.
16. Seng, V., Abbaoui, K. and Cherruault, Y. (1996), "Adomian polynomials for non-linear operators", Mathematical and Computer Modelling, Vol. 24 No. 1, pp. 59-65.