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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

On the instability of leap-frog and Crank-Nicolson approximations of a nonlinear partial differential equation


Author: B. Fornberg
Journal: Math. Comp. 27 (1973), 45-57
MSC: Primary 65M10
MathSciNet review: 0395249
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Abstract: It is well known that nonlinear instabilities may occur when the partial differential equations, describing, for example, hydrodynamic flows, are approximated by finite-difference schemes, even if the corresponding linearized equations are stable. A scalar model equation is studied, and it is proved that methods of leap-frog and Crank-Nicolson type are unstable, unless the differential equation is rewritten to make the approximations quasi-conservative. The local structure of the instabilities is discussed.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1973-0395249-2
PII: S 0025-5718(1973)0395249-2
Keywords: Nonlinear instability, leap-frog scheme, Crank-Nicolson scheme
Article copyright: © Copyright 1973 American Mathematical Society