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Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. (English) Zbl 0832.65098
A new procedure for imposing boundary conditions (simultaneous approximation term) (SAT) that solves a linear combination of the boundary conditions and the differential equations near the boundary is introduced. This technique is an extension of the method used by D. Funaro and D. Gottlieb [Math. Comput. 51, No. 184, 599-613 (1988; Zbl 0699.65079)] to stabilize the pseudospectral Chebyshev collocation method. It is shown that if the approximation of the derivative operator admits a summation-by-parts formula then the SAT method is stable in the classical sense and is also time-stable. The implementation of the SAT method to systems of hyperbolic equations is discussed. Numerical studies are presented to verify the efficacy of the approach.
Reviewer: L.G.Vulkov (Russe)

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
Citations:
Zbl 0699.65079
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