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.


Item Type Articles
CreatorsHill, A.
Related URLs
DepartmentsFaculty of Science > Mathematical Sciences
Research CentresCentre for Action Research in Professional Practice (CARPP)
Bath Institute of Medical Engineering (BIME)
Bath Institute for Complex Systems (BICS)
Bath Economics Research
ID Code26809


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