RESONANCE IN ALMOST LINEAR SYSTEMS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Estimates, useful for all times, are sought for the resonant response of a system with small non-linearity. It is shown that the method of multiple scales can be used to generate a representation which is formally asymptotic at all times and over a significant time interval is a valid approximation to some solution of the system. It is shown, by example that this estimate is not always a useful representation of any one solution for all time. Plausible arguments are given that the approximation is nevertheless useful for the determination of the behavior of a physical system if not of the pathological solutions of the differential equations which may represent it. Author
- Numerical Mathematics