Mathematics – Dynamical Systems
Scientific paper
2009-11-26
SIAM j. on Appl. Dyn.Syst., Vol.8, 1066-1115 (2009)
Mathematics
Dynamical Systems
publised as SIAM j. on Appl. Dyn.Syst., Vol.8, 1066-1115 (2009)
Scientific paper
The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost) periodic vector fields are considered. Theorems on error estimates for approximate solutions, existence of approximate invariant manifolds and their stability, inheritance of symmetries from those for the original equation to those for the RG equation, are proved. Further it is proved that the RG method unifies traditional singular perturbation methods, such as the averaging method, the multiple time scale method, the (hyper-) normal forms theory, the center manifold reduction, the geometric singular perturbation method and the phase reduction. A necessary and sufficient condition for the convergence of the infinite order RG equation is also investigated.
No associations
LandOfFree
Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-116149