A Numerical Dynamical Instability

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  • 1 Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

Errors in the numerical analog to a simple convection model can lead to an instability, even though existing methods of analysis predict that the scheme is stable.

The solutions obtained from a number of finite difference schemes and different resolutions are compared. This shows that increasing the resolution does not significantly improve the results, also that increasing the order of the finite difference scheme can lead to greater errors. The mechanism of the instability is discussed.

Abstract

Errors in the numerical analog to a simple convection model can lead to an instability, even though existing methods of analysis predict that the scheme is stable.

The solutions obtained from a number of finite difference schemes and different resolutions are compared. This shows that increasing the resolution does not significantly improve the results, also that increasing the order of the finite difference scheme can lead to greater errors. The mechanism of the instability is discussed.

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