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Stability theory of difference approximations for multidimensional initial-boundary value problems. (English) Zbl 0563.65064
This paper extends stability results to multidimensional space initial- boundary value problems; the one-dimensional results were obtained by Kreiss among other authors. The hypotheses include here a noncharacteristic boundary and zero initial condition for the differential problem, and the difference approximation is dissipative besides being consistent. The main result is that the multidimensional uniform Kreiss condition (UKC) implies stability; moreover, in the case of constant coefficients, the UKC is shown to be equivalent to the stability of the scheme.
Reviewer: J.P.Milaszewicz

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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