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Is there a way to find out how large the truncation, round-off, and other errors that occur from discretizing a differential equation are while using the default settings in NDSolve? Or would I have to explicitly ask Mathematica to solve the problem using 4th order Runge-Kutta, Adams, etc and find the errors myself.

I did find this link: http://reference.wolfram.com/mathematica/howto/CheckTheResultsOfNDSolve.html

helpful, but I am wondering what other methods are available.

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The last part (Spatial Error Estimates) of this tutorial may be helpful? –  xzczd Mar 27 '14 at 10:49

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