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On the eigensystems associated with numerical boundary schemes for hyperbolic equations. (English) Zbl 0802.76053

Baines, M. J. (ed.) et al., Numerical methods for fluid dynamics 4. Proceedings of the conference held at Reading University, United Kingdom, April 1992. Oxford: Clarendon Press. 473-481 (1993).
The semi-discrete eigenvalue spectra associated with some numerical boundary schemes (NBS’s) are examined. In addition, the effect of the NBS’s on the \(L_ 2\) norm of the semi-discrete solution with initial conditions given by wave packets consisting of Gaussian-modulated cosine functions is studied. The goal of the paper is to demonstrate the effect of NBS’s on semi-discrete solutions of the linear convection equation and to show that NBS’s which are not of maximum order can be advantageous at both inflow and outflow boundaries.
For the entire collection see [Zbl 0787.00028].

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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