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I just have a short question about something:

Which method calculates the more exact result for a differential equation? The Runge-Kutta-method with a constant step-size h or the predictor-corrector-method with the Adams-Bashford- and Adams-Moulton-method? I use the $P(EC)^mE$ method. Does this calculate a better result than the Runge-Kutta-method, even if $m=0$?

I need no proof for that, just the information for a better understanding. I didn't find a comparison, yet.

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    $\begingroup$ For a differential equation? Which one of them, there are like... very may of them! Quite often the best numerical method is best for it's own narrow class of functions. $\endgroup$ – mathreadler Jul 24 '17 at 18:31
  • $\begingroup$ For exemple the function: $$y'=\frac{y-2}{2*t^2-t}$$ with $y(1)=1$, $\endgroup$ – Tobi92sr Jul 24 '17 at 18:42
  • $\begingroup$ I would typically solve a linear least squares using an implicit scheme with some Krylov subspace method over a uniform grid of discretized operators. Not because it is best, but because it is more general. Well, I guess I am not best qualified to answer the question, but good luck. I know there are some guys on here who are good at that. $\endgroup$ – mathreadler Jul 24 '17 at 18:47

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