On the instability of leapfrog and CrankNicolson approximations of a nonlinear partial differential equation
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 by B. Fornberg PDF
 Math. Comp. 27 (1973), 4557 Request permission
Abstract:
It is well known that nonlinear instabilities may occur when the partial differential equations, describing, for example, hydrodynamic flows, are approximated by finitedifference schemes, even if the corresponding linearized equations are stable. A scalar model equation is studied, and it is proved that methods of leapfrog and CrankNicolson type are unstable, unless the differential equation is rewritten to make the approximations quasiconservative. The local structure of the instabilities is discussed.References

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Additional Information
 © Copyright 1973 American Mathematical Society
 Journal: Math. Comp. 27 (1973), 4557
 MSC: Primary 65M10
 DOI: https://doi.org/10.1090/S00255718197303952492
 MathSciNet review: 0395249