Runge-Kutta methods for affinely controlled nonlinear systems

Journal of Computational and Applied Mathematics

Volumn 205, Issue 2, 2007, Pages 957-968

  Kloeden, Peter E ^a   Rößler, Andreas ^b  

^a GOETHE UNIVERSITY   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Affine control; Nonlinear system; Numerical method; Rooted tree analysis; Runge Kutta method

Indexed keywords

COMPUTER SIMULATION; NONLINEAR SYSTEMS; NUMERICAL METHODS; STOCHASTIC CONTROL SYSTEMS;

AFFINE CONTROL; ROOTED TREE ANALYSIS; STOCHASTIC DIFFERENTIAL EQUATIONS;

RUNGE KUTTA METHODS;

EID: 34248156698     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.02.061     Document Type: Article

References (12)

1. Burrage K., and Burrage P.M. High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations. Appl. Numer. Math. 22 (1996) 81-101
2. Colonius F., and Kliemann W. The Dynamics of Control (2000), Birkhäuser, Boston
3. S. Cyganowski, L. Grüne, P.E. Kloeden, MAPLE for stochastic differential equations, in: Theory and Numerics of Differential Equations (Durham, 2000), Universitext, Springer, Berlin, 2001, pp. 127-177. Availability: 〈http://www.uni-bayreuth.de/departments/math/∼lgruene/publ/maplesde.html〉.
4. Ferretti R. Higher-order approximations of linear control systems via Runge-Kutta schemes. Computing 58 (1997) 351-364
5. Grüne L., and Kloeden P.E. Higher order numerical schemes for affinely controlled nonlinear systems. Numer. Math. 89 (2001) 669-690
6. Grüne L., and Kloeden P.E. Pathwise approximation of random ordinary differential equations. BIT 41 4 (2001) 711-721
7. Hairer E., Nørsett S.P., and Wanner G. Solving Ordinary Differential Equations vol. I (1993), Springer, Berlin
8. Isidori A. Nonlinear Control Systems. An Introduction. second ed. (1995), Springer, Heidelberg
9. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations (1992), Springer, Heidelberg (third revised and updated printing, 1999)
10. A. Rößler, Runge-Kutta methods for the numerical solution of stochastic differential equations, Ph.D. Thesis, Darmstadt University of Technology, Shaker Verlag, Aachen, 2003.
11. Rößler A. Stochastic Taylor expansions for the expectation of functionals of diffusion processes. Stochastic Anal. Appl. 22 6 (2004) 1553-1576
12. Rößler A. Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations. Stochastic Anal. Appl. 24 1 (2006) 97-134