The semigroup stability of the difference approximations for initial-boundary value problems

@inproceedings{Wu1995TheSS,
  title={The semigroup stability of the difference approximations for initial-boundary value problems},
  author={Lixin Wu},
  year={1995}
}
  • Lixin Wu
  • Published 1995
  • Mathematics
  • For semidiscrete approximations and one-step fully discretized approximations of the initial-boundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or l 2 stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable Runge-Kutta method is determined by the stability of the semidiscrete approximation 

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    Citations

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 10 REFERENCES

    Stability theory of difference approximations for mixed initial boundary value problems

    • H.-O. Kreiss Gustafsson, A. Sundström
    • Gustafsson , Numerical boundary conditions , Lectures in Appl . Math .
    • 1985

    Numerical boundary conditions

    VIEW 6 EXCERPTS
    HIGHLY INFLUENTIAL

    Agronovich, Theorem of matrices depending on parameters and its application to hyperbolic systems

    • M S.
    • Functional Anal. Appl
    • 1972
    VIEW 1 EXCERPT

    Z-2 is a continuable condition for Kreiss' mixed problems, Comm

    • J. Rauch
    • Pure Appl. Math
    • 1972
    VIEW 1 EXCERPT

    Mixed problems in several variables

    • R. Hersch
    • J. Math. Mech
    • 1963
    VIEW 2 EXCERPTS