Numerical analysis of time discretization of optimal control problems
Numerical analysis of time discretization of optimal control problems
Numerical analysis of time discretization of optimal control problems
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Conditions for order 4<br />
bk<br />
Table 4: Order 4<br />
Graph Condition Graph Condition<br />
1<br />
alkdkdl =<br />
bk<br />
1 <br />
ajkdjck =<br />
8<br />
1<br />
24<br />
bi<br />
aikcidk =<br />
bk<br />
5 <br />
biaijcicj =<br />
24<br />
1<br />
8<br />
<br />
2<br />
cjdj = 1 <br />
bic<br />
12<br />
3 i = 1<br />
<br />
4<br />
1<br />
ckd 2 k = 1 1<br />
d<br />
12<br />
3 l = 1<br />
4<br />
Orders 5 to 7: FB & J. Laurent-Varin (2006), making the link to the<br />
theory <strong>of</strong> partitioned RK schemes and bicolored rooted trees.<br />
b 2 l<br />
43