IMPLICIT-EXPLICIT RUNGE-KUTTA SCHEMES FOR NUMERICAL DISCRETIZATION OF OPTIMAL CONTROL PROBLEMS
Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and nonstiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge-Kutta methods in the context of optimal control problems...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2013-01, Vol.51 (4), p.1875-1899 |
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| container_title | SIAM journal on numerical analysis |
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| creator | HERTY, M. PARESCHI, L. STEFFENSEN, S. |
| description | Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and nonstiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge-Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable transformations of the adjoint equation, order conditions up to order three are proven, and the relation between adjoint schemes obtained through different transformations is investigated as well. Conditions for the IMEX Runge-Kutta methods to be symplectic are also derived. A numerical example illustrating the theoretical properties is presented. |
| doi_str_mv | 10.1137/120865045 |
| format | Article |
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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Adjoints Applied mathematics Coefficients Differential equations Differentials Discretization Hyperlinks Investigations Lagrange multiplier Mathematical analysis Mathematical problems Matrices Methods Numerical analysis Optimal control Optimization Runge Kutta method Transformations |
| title | IMPLICIT-EXPLICIT RUNGE-KUTTA SCHEMES FOR NUMERICAL DISCRETIZATION OF OPTIMAL CONTROL PROBLEMS |
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