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 one-step method<br />
• General one-step method: yk+1 = yk +hkΦ(yk,hk)<br />
• Consistency condition: Φ(y,0) = f(y)<br />
• Taylor expansion: yk+1(h) = yk +hf(yk)+ 1<br />
2 h2 ···<br />
• Global error order: maximum power for which the expansion <strong>of</strong> the<br />
scheme coincides with the one <strong>of</strong> the ODE<br />
• Euler method: Φ(y,h) = f(y).<br />
Error order 1, principal error term 1<br />
2 h2 f ′ f.<br />
• General case: <strong>analysis</strong> based on the theory <strong>of</strong> rooted trees.<br />
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