Diagonalization and simultaneous symmetrization of the gas-dynamic matrices

Authors:
R. F. Warming, Richard M. Beam and B. J. Hyett

Journal:
Math. Comp. **29** (1975), 1037-1045

MSC:
Primary 76.35

DOI:
https://doi.org/10.1090/S0025-5718-1975-0388967-5

MathSciNet review:
0388967

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Abstract: The hyperbolicity of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation which diagonalizes an arbitrary linear combination of coefficient matrices . The matrix *T* that accomplishes this transformation is given explicitly, and the spectral norms of *T* and are computed. It is also shown that the individual matrices are simultaneously symmetrized by the same similarity transformation. Applications of the transformations *T* and and their norms include the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, construction of difference schemes based on characteristic relations, and simplification of the solution of block-tridiagonal systems that arise in implicit time-split algorithms.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0388967-5

Keywords:
Hyperbolic partial differential equations,
initial-value problems,
inviscid flows,
construction and stability of finite-difference schemes,
similarity transformation

Article copyright:
© Copyright 1975
American Mathematical Society