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- W2065648743 abstract "It is known that the stability of finite-difference models of hyperbolic initial-boundary value problems is connected with the propagation and reflection of parasitic waves. Here the waves point of view is applied to models containing two boundaries or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Our analysis accounts for various known instability phenomena in a unified way and leads to several new results, three of which are as follows. (1) Dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface. (2) Algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present. (3) GKS-stability and <italic>P</italic>-stability can be established in certain problems by showing that the numerical reflection coefficient matrices have norm less than one." @default.
- W2065648743 created "2016-06-24" @default.
- W2065648743 creator A5065363123 @default.
- W2065648743 date "1985-01-01" @default.
- W2065648743 modified "2023-09-27" @default.
- W2065648743 title "Stability of finite-difference models containing two boundaries or interfaces" @default.
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- W2065648743 doi "https://doi.org/10.1090/s0025-5718-1985-0804924-2" @default.
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