I have a review question that asks us to find the order of this iterative method: $U^{n+3}=U^n+\frac{3}{8}h[f^{n+3}+3f^{n+2}+3f^{n+1}+f^n]$. I really do not understand how to do this, since we've talked about the method of $\frac{|x_{n+1}-x^*|}{|x_n-x^*|^p}=L$, where p is the order of convergence, but I do not understand how to do this with this method. Could someone explain how this applies to our method? I don't need an answer, just an explanation on how to apply the concept!
Asked
Active
Viewed 105 times
0
-
This is a linear multistep method for differential equations. You need to apply the specific consistency and convergence properties. – Lutz Lehmann May 01 '18 at 07:19
-
Would it be sufficient to find $/tau_n$ being of order $k^p$ and then we know the LMM is of order p? – bananagurlz May 01 '18 at 18:14
-
Yes, that would be sufficient. However, note that this method is not stable, as period 3 oscillations may persist and accumulate from floating point noise. – Lutz Lehmann May 01 '18 at 18:59