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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Order <strong>of</strong> a RK scheme II<br />
• By induction: explicit expansion, using<br />
q<br />
ℓ=0<br />
h q<br />
q! ykiq = yk +h<br />
s<br />
j=1<br />
aij<br />
q−1<br />
ℓ=0<br />
f(ykj(h))+O(h q+1 ).<br />
• Expansion: linear combination <strong>of</strong> the elementary differentials (as<br />
for the solution <strong>of</strong> the ODE)<br />
• Global error order p iff, in the expansion <strong>of</strong> yk+1, these coefficients<br />
coincide up to order p.<br />
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