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Mathematics of Computation

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Contractive difference schemes for symmetric hyperbolic systems

Authors: Philip Brenner and Vidar Thomée
Journal: Math. Comp. 25 (1971), 205-217
MSC: Primary 65N05
MathSciNet review: 0297151
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Abstract: Consider the initial-value problem for a constant-coefficient symmetric hyperbolic system with initial-values vanishing in a half-space. Consider also a finite difference operator consistent with the system. Conditions are given in terms of the orders of dissipation and accuracy which ensure that the solution of the discrete problem tends to zero exponentially with the mesh-width in half-spaces where the solution of the continuous problem vanishes.

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Keywords: Symmetric hyperbolic system, initial-value problem, difference scheme, contractive, dissipative, stability, accuracy, Fourier transform
Article copyright: © Copyright 1971 American Mathematical Society