Diagonalization and simultaneous symmetrization of the gas-dynamic matrices
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- by R. F. Warming, Richard M. Beam and B. J. Hyett PDF
- Math. Comp. 29 (1975), 1037-1045 Request permission
Abstract:
The hyperbolicity of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation which diagonalizes an arbitrary linear combination $\Sigma {k_j}{A_j}$ of coefficient matrices ${A_j}$. The matrix T that accomplishes this transformation is given explicitly, and the spectral norms of T and ${T^{ - 1}}$ are computed. It is also shown that the individual matrices ${A_j}$ are simultaneously symmetrized by the same similarity transformation. Applications of the transformations T and ${T^{ - 1}}$ 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.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- 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