Numerical study of Lorenz's equation by the Adomian method

Computers and Mathematics with Applications

Volumn 33, Issue 3, 1997, Pages 25-29

  Guellal, S ^a   Grimalt, P ^b   Cherruault, Y ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF ALICANTE   (Spain)

Author keywords

Adomian's polynomials; Decomposition method; Differential system; Lorenz equations; Runge Kutta technique

Indexed keywords

MATHEMATICAL MODELS; NUMERICAL ANALYSIS; POLYNOMIALS;

ADOMIAN'S POLYNOMIALS; LORENZ EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0031072223     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(96)00234-9     Document Type: Article

References (15)

1. G. Adomian, Nonlinear Stochastic Systems and Application to Physics, Kluwer, (1989).
2. G. Adomian, A review of the decomposition method and some results for nonlinear equations, Mathl. Comput. Modelling 13 (7), 17-43 (1990).
3. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, (1994).
4. K. Abbaoui and Y. Cherruault, Convergence of Adomian's method applied to differential equations, Mathl. Comput. Modelling 28 (5), 103-109 (1994).
5. K. Abbaoui and Y. Cherruault, New ideas for proving convergence of decomposition methods, Computers Math. Applic. 29 (7), 103-108 (1995).
6. Y. Cherruault, Convergence of Adomian's method, Kybernetes 18 (2), 31-38 (1989).
7. Y. Cherruault and G. Adomian, Decomposition method: A new proof of convergence, Mathl. Comput. Modelling 18 (12), 103-106, (1993).
8. Y. Cherruault G. Adomian, K. Abbaoui and R. Rach, Further remarks on convergence of decomposition, I.J.B.C. 38, 89-93 (1995).
9. S. Guellal and Y. Cherruault, Practical formulae for calculation of Adomian's polynomials and application to the convergence of the decomposition method, I.J.B.C. 36, 223-228 (1994).
10. K. Abbaoui, Y. Cherruault and V. Seng, Practical formulae for the calculus of multivariable Adomian's polynomials, Mathl. Comput. Modelling 22 (1), 89-93 (1995).
11. K. Abbaoui, Y. Cherruault and M. N'Dour, The decomposition method applied to differential equation systems, Kybernetes 24 (8), 32-40 (1995).
12. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Stranger Attractors, Springer-Verlag, (1985).
13. P. Grimalt, Hacia modelaciones matemáticas del músculo cardiaco: Bases y teorías que lo fundamentan, Fundación general de la Universidad Complutense de Madrid, Cursos de verano del Escorial, Madrid (to appear).
14. D. Kaplan and L. Glass, Understanding Non-Linear Dynamics, Springer-Verlag, (1995).
15. S. Guellal and Y. Cherruault, Application of the decomposition method to identify the distributed parameters of elliptical equation, Mathl. Comput. Modelling 21 (4), 51-55 (1994).