Abstract
We show that MacCormack's method for the scalar advection equation u t = au x + bu y is stable if (aΔt/Δx) 2 + (bΔt/Δy) 2 ≤ 2 1+ 1 8 −2≈ 1 8 . This bound on the mesh ratios is not optimal, since numerical sampling shows that .3266 will do when ( aΔ t/Δ x) 2 = ( bΔ t/Δ y) 2.
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