Numerical Instability due to Varying Time Steps in Explicit Wave Propagation and Mechanics Calculations

Explicit central-difference time integration is frequently used to solve the wave equation, and the classical criterion for numerical stability is the Courant–Friedrichs–Lewy condition. Similarly, explicit integration of a spring-mass mechanical system has a stability condition. These conditions are...

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Bibliographic Details
Published in:Journal of computational physics 1998-03, Vol.140 (2), p.421-431
Main Author: Wright, Joseph P.
Format: Article
Language:English
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Summary:Explicit central-difference time integration is frequently used to solve the wave equation, and the classical criterion for numerical stability is the Courant–Friedrichs–Lewy condition. Similarly, explicit integration of a spring-mass mechanical system has a stability condition. These conditions are derived under the assumption of constant time steps. This paper demonstrates the new and perhaps surprising result that numerical instability may occur when time steps vary, even though all steps are substantially less than the constant step criterion.
ISSN:0021-9991
1090-2716
DOI:10.1006/jcph.1998.5902