I just started studying RK method of order 2. I want to know that, " RK method of order 2 and 2 step RK method are same or not?"

  • 1
    $\begingroup$ It's not usually called the 'two step RK method', rather, the 'two stage RK method'. $\endgroup$
    – mattos
    Apr 4 '17 at 10:42
  • $\begingroup$ You can easily construct 2-stage RK methods that only have order $1$. I think it starts with order $6$ that there are no p-stage methods of order $p$. $\endgroup$ Apr 4 '17 at 12:15
  • $\begingroup$ @Mattos y_n+1 = y_n + 1/2(K0+K1) is this a 2 step method or 3 step method? $\endgroup$ Apr 4 '17 at 16:56
  • $\begingroup$ Two function evaluations = two stages. $\endgroup$ Apr 6 '17 at 7:45

Steps/stages = number of function evaluations.

Order = accuracy of the approximation.

The usual RK2 requires two evaluations and the error is $O(h^2)$ ($h =$ step size.)


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