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One of the mysteries that my numerics class left me with are "stiff systems". Our prof didn't really manage to explain what they are. Now that the class (and the test) are over, I'm still curious.

The most concise definition about "stiff systems" I've found so far is: "There is no universally accepted definition of stiffness". So, if there is none, I don't expect one.

I'd be thankful about information on both of the following points:

  • From what kind of (real-world) problems do stiff systems arise? What's so "stiff" about them?
  • What's the good thing - or the bad thing - that I'd worry about when I have to numerically solve such a real-world problem?
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    A tutorial on [stiffness detection](http://reference.wolfram.com/mathematica/tutorial/NDSolveStiffnessTest.html) in _Mathematica_'s `NDSolve` makes for an interesting and useful read.2012-05-03
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    The question was [discussed nicely at scicomp.SE](http://scicomp.stackexchange.com/questions/891); personally, I stick with the working definition "it's stiff if explicit methods perform inefficiently on it".2012-05-04

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