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On the Importance of the Dynamics of DiscretizationsIt has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.
Document ID
20020024909
Acquisition Source
Ames Research Center
Document Type
Conference Paper
Authors
Sweby, Peter K.
(Reading Univ. United Kingdom)
Yee, H. C.
(NASA Ames Research Center Moffett Field, CA United States)
Rai, ManMohan
Date Acquired
August 20, 2013
Publication Date
January 1, 1995
Subject Category
Numerical Analysis
Meeting Information
Meeting: 3rd International Congress on Industrial and Applied Mathematics
Location: Hamburg
Country: Germany
Start Date: July 3, 1995
End Date: July 7, 1995
Funding Number(s)
PROJECT: RTOP 505-59-53
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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