Parametric excitation of computational mode of the leapfrog scheme applied to the Van der Pol equation
type: Item
instance of: scholarly article
title: Parametric excitation of computational mode of the leapfrog scheme applied to the Van der Pol equation
zbMATH Open document ID: 0782.65100
author: Akira Aoyagi
author: Kanji Abe
author: Dong Sheng Cai
published in: Journal of Computational Physics
publication date: 1994-03-07T00:00:00Z
review text: 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.
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 404856
zbMATH Keywords: leapfrog scheme
zbMATH Keywords: Van der Pol equation
zbMATH Keywords: oscillation
zbMATH Keywords: stability
zbMATH Keywords: Runge- Kutta smoother
zbMATH Keywords: longtime integration
MaRDI profile type: Publication
full work available at URL: jcph.1993.1131
OpenAlex ID: W2042424270
DOI: 10.1006/JCPH.1993.1131
description: scientific article; zbMATH DE number 404856