Higher order numerical schemes for affinely controlled nonlinear systems

L. Grüne, P. E. Kloeden: Higher order numerical schemes for affinely controlled nonlinear systems
Numerische Mathematik 89, 669 - 690, 2001

DOI: 10.1007/s002110000279
Keywords: affinely controlled nonlinear systems; stochastic Taylor expansion; Fliess expansion; numerical Taylor schemes; Runge-Kutta schemes
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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.

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