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Parametric Excitation of Computational Mode of the Leapfrog Scheme Applied to the Van der Pol Equation

✍ Scribed by DongSheng Cai; Akira Aoyagi; Kanji Abe

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 212 KB
Volume: 107
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1993.1131

No coin nor oath required. For personal study only.

✦ Synopsis

The leapfrog scheme is applied to the Van der Pol equation. When the amplitude of oscillation of the physical mode exceeds a critical value, the computational mode is parametrically excited by the physical mode. The growth of the computational mode interrupts the integration based on the leapfrog scheme. The critical amplitude of the physical mode is determined by the linear stability analysis and the parametric excitation theory. The Runge-Kutta smoother eliminating the computational mode enables the longtime integration based on the leapfrog scheme. (C) 1993 Acadernic Press; Inc.

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