The Renormalization Group Method for Ordinary Differential Equations

Part of the Mathematics for Industry book series (MFI, volume 5)


The renormalization group (RG) method is one of the singular perturbation methods which provides asymptotic behavior of solutions of differential equations. In this article, how to construct approximate solutions by the RG method is shown with several examples and basic theorems on the RG method, such as an error estimate and the existence of invariant manifolds are given.


Renormalization group Dynamical systems Perturbation method 


  1. 1.
    H. Chiba, Extension and unification of singular perturbation methods for ODEs based on the renormalization group method. SIAM J. Appl. Dyn. Syst. 8, 1066–1115 (2009)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    H. Chiba, Reduction of weakly nonlinear parabolic partial differential equations. J. Math. Phys. 54, 101501 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    L.Y. Chen, N. Goldenfeld, Y. Oono, Renormalization group and singular perturbations: multiple scales, boundary layers, and reductive perturbation theory. Phys. Rev. E 54, 376–394 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

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