Accuracy bounds for semidiscretizations of hyperbolic problems

Jeltsch, Rolf; Strack, Klaus-Günther

doi:10.1090/S0025-5718-1985-0804929-1

Accuracy bounds for semidiscretizations of hyperbolic problems
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by Rolf Jeltsch and Klaus-Günther Strack PDF

Math. Comp. 45 (1985), 365-376 Request permission

Abstract:

Bounds are given for the error constant of stable finite-difference methods for first-order hyperbolic equations in one space dimension, which use r downwind and s upwind points in the discretization of the space derivatives, and which are of optimal order $p = \min (r + s,2r + 2,2s)$ . It is known that this order can be obtained by interpolatory methods. Examples show, however, that their error constants can be improved.

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