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Mathematics of Computation

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

Author: Lixin Wu
Journal: Math. Comp. 64 (1995), 71-88
MSC: Primary 65N06; Secondary 34G10, 65N12
MathSciNet review: 1257582
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Abstract: 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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Keywords: Hyperbolic, semigroup stability, Runge-Kutta methods
Article copyright: © Copyright 1995 American Mathematical Society

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