Validity of the multiple scale method for very long intervals

DOI10.1007/BF00915274zbMath0867.34033MaRDI QIDQ2365365

Lih-Chyun Wang, James A. Murdock

Publication date: 11 August 1997

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

method of averagingmultiple scale methodnonlinear oscillation problems

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items

Working with multiscale asymptotics ⋮ Distinguished limits and drifts: between nonuniqueness and universality

Cites Work

• Improved N-th order averaging theory for periodic systems
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• On the length of validity of averaging and the uniform approximation of elbow orbits, with an application to delayed passage through resonance
• Two-timing on the half line for damped oscillation equations
• Shadowing multiple elbow orbits: An application of dynamical systems to perturbation theory
• A shadowing approach to passage through resonance
• Some Asymptotic Estimates for Higher Order Averaging and a Comparison with Iterated Averaging
• Asymptotic Approximations and Extension of Time-Scales
• On a Derivative-Expansion Technique and Some Comments on Multiple Scaling in the Asymptotic Approximation of Solutions of Certain Differential Equations
• On a common derivation of the averaging method and the two-timescale method
• Some foundational issues in multiple scale theory
• Higher Order Averaging and Related Methods for Perturbed Periodic and Quasi-Periodic Systems
• Averaging methods in nonlinear dynamical systems
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