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This paper deals with a new proof of convergence of Adomian’s method applied to differential equations. We also give new formulae and properties, and we suggest a simple computational form for Adomian’s polynomials.
In this paper, we give new formulae which calculate easily the Adomian's polynomials used in decomposition methods. Then, the proof of convergence of the Adomian's technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation.
Many bio-medical models lead to differential systems where some parameters have to be identified from partial observation on the system's solution. For two- or three-compartment models parameters to be identified can be explicitly calculated (when uniqueness is ensured) from the algebraic relation obtained by using classical methods. However, when the… (More)
The decomposition method solves a wide class of nonlinear functional equations. This method uses a series solution with rapid convergence. This paper is intended as a useful review and clarification of related issues.