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 , 2 r + 2 , 2 s ) 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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