ExerciseODEsadvanced

Exercise: AB2 and order estimation

Solving a logistic IVP (Verhulst) with AB2 started with Heun and estimating the order numerically by doubling the number of subintervals.

Estimating the order

For the IVP $y'(t)=(3-0.1\,y)\,y$ , $t\in[0,2]$ , $y(0)=10$ (Verhulst model, the same as in the one-step methods exercise), solve with AB2 for $N=\{2,4,8,16,32,64\}$ subintervals, starting $y_1$ with Heun, and estimate the order from the ratio of maximum errors when doubling $N$ .

N	Maximum error $E_N$	$\log_2(E_{N/2}/E_N)$
2	10.1480	n/a
4	4.5230	1.1658
8	0.6324	2.8384
16	0.1938	1.7064
32	0.0543	1.8365
64	0.0144	1.9178