Linear multistep approximation of nonsymmetric rotating systems
Hill, A., 2009. Linear multistep approximation of nonsymmetric rotating systems. JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics, 4 (1-2), pp. 103-112.
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This paper considers the stability of one-leg linear multistep methods applied to linear nonautonomous systems of equations, in which the governing matrix is nonsymmetric and is subject to a constant rotation. It is shown that the stability of the underlying system and of the one--leg methods may be analysed using eigenvalues, following a transformation to a rotating frame. For 2-dimensional systems, general conditions for numerical instability are derived. Stable systems are constructed that are unstable for the Backward Euler and BDF2 methods. A family of neutrally stable systems is identified that is numerically unstable for the BDF3 and BDF4 methods, for all sufficiently small step sizes.
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