Numerical Schemes of Higher Order for a Class of Nonlinear Control Systems

  • Lars Grüne
  • Peter E. Kloeden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)


We extend a systematic method for the derivation of high order schemes for affinely controlled nonlinear systems to a larger class of systems in which the control variables are allowed to appear nonlinearly in multiplicative terms. Using an adaptation of the stochastic Taylor expansion to control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Lars Grüne
    • 1
  • Peter E. Kloeden
    • 1
  1. 1.Fachbereich MathematikJ.W. Goethe-UniversitätFrankfurt am MainGermany

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