Abstract
The author's earlier paper on the N-Body problem [1] showing that the dynamics of N bodies in a gravitational field are calculable by the decomposition method [2] is extended and clarified further with a simpler, more computationally convenient treatment of the necessary special polynomials.
Similar content being viewed by others
References
G. Adomian, “The N-body problem,”Found. Phys. Lett 6(6) 597–602, 1993.
G. Adomian,Solving Frontier Problems of Physics: The Decomposition Method (Kluwer Academic, Dordrecht, 1994).
K. Abbaoui, “Les fondements mathematiques la méthode decompositionnelle d'Adomian et application à la resolution de problemes issus de la biologie et de la medicine,” Thesis, Université Paris VI, Institut Pierre et Marie Curie, 1995.
K. Abbaoui and Y. Cherruault, “Convergence of Adomian's method applied to differential equations,”Math. Comput. Modelling 28(5), 103–109 (1994).
K. Abbaoui and Y. Cherruault, “New ideas for proving convergence of decomposition Methods,”Computers Math. Applic. 29 (7), 103–108 (1995).
K. Abbaoui and Y. Cherruault, “Convergence of Adomian's method applied to nonlinear equations,”Math. Comput. Modelling 20(9), 60–73 (1994).
K. Abbaoui, Y. Cherruault, and V. Seng, “Practical formulae for the calculus of multivariable Adomian polynomials,”Math. Comput. Modelling, to appear.
K. Abbaoui, Y. Cherruault, and M. N'Dour, “The decomposition method applied to differential equations systems,”Kybernetes, to appear.
G. Adomian,Nonlinear Stochastic Operator Equations (Academic, New York, 1986).
G. Adomian,Stochastic Systems (Academic, New York, 1983).
G. Adomian,Nonlinear Stochastic Systems and Applications to Physics (Kluwer Academic, Dordrecht, 1989).
G. Adomian, “Convergent series solutions on nonlinear equations,”Computers Math. Applic. 11 2 1984.
G. Adomian, “On composite nonlinearities and the decomposition method,”J. Math. Anal. Applic. 114 (1) (1986).
G. Adomian, “An efficient methodology for the physical sciences,”Kybernetes,20 (7), 24–34 (1991).
G. Adomian and R. Rach, “Generalization of Adomian polynomials to functions of several variables,”Computers Math. Applic. 24 (516), 11–24 1992.
R.E. Bellman and G. Adomian,Partial Differential Equations - New Methods for Their Treatment and Applications (Reidel, Dordrecht, 1986).
Y. Cherruault, G. Adomian, K. Abbaoui, and R. Rach, “Further remarks on convergence of the decomposition method,”I.J.B.C. 38, 89–93 (1995).
Y. Cherrault and G. Adomian, “Decomposition method: A new proof of convergence,”Math. Comput. Modelling 18 (12), 103–106 (1993).
Y. Cherruault, “Convergence of Adomian's method,”Kybernetes 18 (2), 31–38 (1989).
Y. Cherruault, G. Saccomandi and B. Some, “New results for convergence of Adomian's method applied to integral equations,”Mathl. Comput. Modelling 16 (2), 85–93 (1992).
“Modelisation Mathematiques de la Diffusion des Medicaments a travers les Capillaires et dans les Tissus à la suite d'une Injection et Equisse d'une Theorie Decompositionnelle et Applications aux Equations aux Derivces Partielles”, These de l'Ecole Centrale de Paris, 1992.
L. Gabet, “The theoretical foundation of the Adomian method,”Computers Math. Applic. 27 (12), 41–52 (1994).
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).
T. Mavoungou and Y. Cherruault, “Convergence of Adomian's method applied to nonlinear partial differential equations,”Kybernetes 21 (6), 13–25(1992).
V. Seng, K. Abbaoui and Y. Cherruault, “Adomian's polynomials for nonlinear operators,”Math. Comput. Modelling, to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Adomian, G. A non-perturbative solution of N-Body dynamics. Found Phys Lett 9, 301–308 (1996). https://doi.org/10.1007/BF02186409
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02186409