On the Stability of the N Cycle Scheme of Lorenz

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  • 1 Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, Mass. 02139
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Abstract

The stability of the N-cycle scheme of Lorenz for hyperbolic systems of partial differential equations and for parabolic equations is explored. Stability conditions are given explicitly. For hyperbolic systems, the results indicate that the fourth-order scheme is the most efficient. For the parabolic equation the results indicate that the stability condition is not, as was suggested by Lorenz, independent of N.

Abstract

The stability of the N-cycle scheme of Lorenz for hyperbolic systems of partial differential equations and for parabolic equations is explored. Stability conditions are given explicitly. For hyperbolic systems, the results indicate that the fourth-order scheme is the most efficient. For the parabolic equation the results indicate that the stability condition is not, as was suggested by Lorenz, independent of N.

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