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The Galerkin‐averaging method for nonlinear, undamped continuous systems
Author(s) -
Stroucken A. C. J.,
Verhulst F.,
Eckhaus W.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090134
Subject(s) - mathematics , galerkin method , nonlinear system , mathematical analysis , method of averaging , boundary value problem , projection (relational algebra) , extension (predicate logic) , order (exchange) , projection method , resonance (particle physics) , dykstra's projection algorithm , mathematical optimization , physics , algorithm , finance , quantum mechanics , particle physics , computer science , economics , programming language
The analysis of initial‐boundary value problems for nonlinear evolution equations with a small parameter is carried out by projection and averaging. The complications of the extension to a second order approximation is discussed and subsequently demonstrated for the perturbed Klein‐Gordon equation. The difference between the case of resonance and nonresonance at first order is emphasized.