Poincaré–Lindstedt method
Technique used in perturbation theory / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Poincaré–Lindstedt method?
Summarize this article for a 10 year old
In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail. The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear[disambiguation needed] problems with finite oscillatory solutions.[1][2]
The method is named after Henri Poincaré,[3] and Anders Lindstedt.[4]
All efforts of geometers in the second half of this century have had as main objective the elimination of secular terms.
— Henri Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, preface to volume I
The article gives several examples. The theory can be found in Chapter 10 of Nonlinear Differential Equations and Dynamical Systems by Verhulst.[5]