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Linear Advection – The Story So Far ...<br />
second order schemes:<br />
modified equation: dispersive equation<br />
∂ <br />
∂t<br />
u ∂ <br />
∂ x = ∂3 <br />
∂ x 3<br />
→ oscillating behaviour of the numerical solution<br />
waves:<br />
group velocity<br />
c g = u + 3µ k2<br />
µ < 0 µ > 0<br />
c g < u<br />
c g > u
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