Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I

Goldberg, Moshe; Tadmor, Eitan

doi:10.1090/S0025-5718-1978-0501998-X

Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I
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by Moshe Goldberg and Eitan Tadmor PDF

Math. Comp. 32 (1978), 1097-1107 Request permission

Abstract:

Easily checkable sufficient stability criteria are obtained for explicit dissipative approximations to mixed initial-boundary value problems associated with the system ${u_t} = A{u_x}$ in the quarter plane $x \geqslant 0$, $t \geqslant 0$. The criteria are given entirely in terms of the boundary conditions for the outflow unknowns. The results imply that certain well-known boundary conditions, when used in combination with any (stable) dissipative scheme, always maintain stability.

References

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How the Boundary Conditions Affect the Stability and Accuracy of Some Implicit Methods for Hyperbolic Equations