Pseudospectral method vs spectral method

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What is the difference between the two?
When would I use one over the other?
 
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For what?
 
Say for I wanted to look at the time evolution of a wave equation to the
non-linear schrodinger equation. Or even the regular schrodinger equation.
 

Thread 'Is a table levitating possible, even at a minuscule probability?'

I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
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