Higher order numerical schemes for affinely controlled nonlinear systems

Titelangaben

Grüne, Lars ; Kloeden, Peter E.:
Higher order numerical schemes for affinely controlled nonlinear systems.
In: Numerische Mathematik. Bd. 89 (2001) . - S. 669-690.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s002110000279

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Abstract

A systematic method for the derivation of high order schemes for affinely controlled nonlinear systems is developed. Using an adaptation of the stochastic Taylor expansion for control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained. Furthermore an approximation technique for the multiple control integrals appearing in the schemes is proposed.