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Advection Equation: An overview: 

 

Analytical:

\(\frac{\partial u}{\partial t}-c\frac{\partial u}{\partial x}\)

solution: \(u(t,x)=f(x-ct)\) 

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Euler forward: Only stable when with upstream space differencing. Introduces a strong damping. The CFL criterion must be also fulfilled. 

Leap-frog scheme: conditionally stable with the CFL criterion. 

Fazit: I would use leapfrog since it has a higher order of accuracy than the others.