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An accelerated Poincaré-map method for autonomous oscillators. (English) Zbl 1027.65109
Summary: A novel time-domain method for finding the periodic steady state of a free-running electrical oscillator is introduced. The method is based on the extrapolation technique MPE. The new method is applied to a family of artificial benchmark problems and to a real circuit (Colpitt’s oscillator). It turns out to have super-linearly convergence properties in both cases. Full implementational details are provided.

MSC:
65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems
34A09 Implicit ordinary differential equations, differential-algebraic equations
78A55 Technical applications of optics and electromagnetic theory
34C25 Periodic solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
Software:
SPECTRE; SPICE
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References:
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