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Robotics

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    $\begingroup$ I suspect mainly because Euler is only second order method. This means it requires significant more simulation steps in order to get the same accuracy as ode45. Also ode45 has a variable stepsize, such that the local error is also roughly constant which also requires less simulation steps. You can test this yourself by looking at the computation time of both. $\endgroup$ Commented Apr 12, 2015 at 1:13
  • $\begingroup$ @fibonatic: Euler method is second order accurate locally. Globally (accumulating errors over multiple time steps), it is much worse: only first order accuracy. $\endgroup$ Commented Apr 12, 2015 at 16:08
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    $\begingroup$ This question is more appropriate for the SciComp SE site, since it has more to do with numerical methods than robotics. I recommend posting future questions of this type there. $\endgroup$ Commented Apr 12, 2015 at 20:49
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    $\begingroup$ In a real control setting, that is with a digital controller and therefore not dealing with any simulation, you must work with constant sample time. In this regard, Tustin integration (bilinear transformation) has a wider application than forward or backward Euler formula. $\endgroup$ Commented Apr 13, 2015 at 18:20
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    $\begingroup$ I think there's more than that behind. For a complete overview refer to wikipedia. For a comparison between Euler's and Tustin's formulas, refer to this page. $\endgroup$ Commented Apr 14, 2015 at 9:03