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I have a system of nonlinear first-order autonomous IVP ordinary differential equations for which I'll solve numerically since I can't obtain a closed-form solution.

What are the notions that matters most when comparing candidate numerical methods in this particular case? Will I be able to obtain a more refined answer given the system at hand?

What are the tools used to quantitatively estimate the errors (locally and globally)?

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    @J.M. Great, tha$n$ks.2011-09-25

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