I am solving a 1D advection problem of the the form $$d{Q}/dt = [A]{Q}$$ where {Q} is the vector of unknowns and [A] is the matrix of coefficients of spatial discretisation. I have worked out the eigenvalues of [A] to get an idea about the stability of the semi-discretised system and I am getting eigenvalues with positive real parts plus imaginary parts. I know positive real parts are a sign of instability, but my results show the smooth travelling of a wave. I wanted to know what conclusions I can draw from this? Thanks!

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    $\begingroup$ You can only conclude that either your analysis or your code (or both) is incorrect. $\endgroup$ – David Ketcheson Sep 14 '15 at 16:27
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    $\begingroup$ The correct word is "instability", not "insatiability" (even though the latter would be an interesting choice as well). $\endgroup$ – Wolfgang Bangerth Sep 14 '15 at 18:42
  • $\begingroup$ @David, how about when the eigenvalues are zero? Are there any good references for this? $\endgroup$ – melody Sep 21 '15 at 11:13
  • $\begingroup$ You mean $A$ is diagonalizable and all eigenvalues are zero? Then $A$ is the zero matrix and the problem is trivial. If you want to ask another question, either edit your question or start a new one. Comments are not questions. $\endgroup$ – David Ketcheson Sep 21 '15 at 12:45
  • $\begingroup$ Sorry, I meant what if the real parts are zero? (the question is pretty similar, can I change the heading of this one? ) $\endgroup$ – melody Sep 21 '15 at 12:50

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