Duffing's Equation and Nonlinear Resonance

Autor/in	Fay, Temple H.
Titel	Duffing's Equation and Nonlinear Resonance
Quelle	In: International Journal of Mathematical Education in Science and Technology, 34 (2003) 6, S.871-880 (10 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Equations (Mathematics); Calculus; Error of Measurement; Problem Solving; Mathematics Instruction; Matrices + Suchen Sie Ihr Suchwort? Equations; Mathematics; Gleichungslehre; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Messfehler; Problemlösen; Mathematics lessons; Mathematikunterricht; Matrizenrechnung
Abstract	The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto an unbounded one. This is a common occurrence when numerically solving differential equations with initial values very close to a separatrix that distinguishes between stable (bounded) solutions and unstable (unbounded) solutions. This numerical phenomenon is not discussed in most texts and it is the purpose of this article to describe the effect is such a way as to make it suitable for beginning students to understand why things happen the way they do. Given the modern trend for computer laboratory projects in beginning differential equations courses, it is important for students to be aware of one of the common failings of numerical solutions. (Contains 4 figures.) (Author).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10