On a certain renormalization group method
M. Ziane
Source abstract
In this paper, a mathematical study of the renormalization group method, recently introduced by Chen, Goldenfeld, and Oono [Phys. Rev. E 54, 376 (1997); Phys. Rev. Lett. 73, 1311 (1994), NATO Adv. Study Inst. Ser., Ser. B 284, 375 (1991)] is given for the case of autonomous nonlinear systems of differential equations. We also observe that the approximation results obtained by this method by Chen, Goldenfeld, and Ono [NATO Adv. Study Inst. Ser., Ser. B 284, 375 (1991)] are valid over long time intervals. Moreover, a connection between this method and the classical Poincaré–Dulac normal forms and the averaging method is briefly discussed.
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