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An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPsThe eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.
Document ID
19900003821
Acquisition Source
Legacy CDMS
Document Type
Technical Memorandum (TM)
Authors
Warming, Robert F.
(NASA Ames Research Center Moffett Field, CA, United States)
Beam, Richard M.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
September 6, 2013
Publication Date
October 1, 1989
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.15:102241
NASA-TM-102241
A-89259
Meeting Information
Meeting: GAMM Conference on Numerical Methods in Fluid Mechanics
Location: Delft
Country: Netherlands
Start Date: September 27, 1989
End Date: September 29, 1989
Accession Number
90N13137
Funding Number(s)
PROJECT: RTOP 505-60-00
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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