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Multiple-scale analysis

In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables. This is done by introducing fast-scale and slow-scale variables for an…

Differential equation and energy conservation, Solution & Straightforward perturbation-series solution

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Differential equation and energy conservation

Duffing equationOrdinary differential equationNonlinearOscillatorHamiltonian system
6 related topics

Solution

Complex-valued amplitudeRight hand sideComplex conjugateFrequencyLindstedt–Poincaré method
6 related topics

Straightforward perturbation-series solution

Order of magnitudeLeading-order
2 related topics

Coordinate transform to amplitude/phase variables

Method of normal forms
1 related topics

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Overview

Differential equation and energy conservation

Straightforward perturbation-series solution

Solution

Coordinate transform to amplitude/phase variables

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Multiple-scale analysis

Nodes29
Edges28
Triples11
Avg. degree1.93
Density0.068966
Components1

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Multiple-scale analysis

Top relations

related to Differential equation and energy conservation · 7
Multiple-scale analysis → As, Consequently, Duffing, H0, Hamiltonian, The, This
related to Method of multiple scales · 4
Multiple-scale analysis → Introduce, Similarly, So, To

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Important terminology

displaystyle solution varepsilon frac method dt equation variables right mathcal analysis multiple coordinate left perturbation slow independent duffing amplitude also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Multiple-scale analysisrelated to Differential equation and energy conservationAs0.60section
Multiple-scale analysisrelated to Differential equation and energy conservationDuffing0.60section
Multiple-scale analysisrelated to Differential equation and energy conservationThe0.60section
Multiple-scale analysisrelated to Differential equation and energy conservationHamiltonian0.60section
Multiple-scale analysisrelated to Differential equation and energy conservationConsequently0.60section
Multiple-scale analysisrelated to Differential equation and energy conservationH00.60section
Multiple-scale analysisrelated to Differential equation and energy conservationThis0.60section
Multiple-scale analysisrelated to Method of multiple scalesTo0.60section
Multiple-scale analysisrelated to Method of multiple scalesIntroduce0.60section
Multiple-scale analysisrelated to Method of multiple scalesSo0.60section
Multiple-scale analysisrelated to Method of multiple scalesSimilarly0.60section

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    Min side: 3
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