A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

BIT Numerical Mathematics

Volumn 37, Issue 4, 1997, Pages 771-780

  Burrage, K ^a   Burrage, P M ^a   Belward, J A ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Runge Kutta methods; Stochastic ordinary differential equation; Strong order

Indexed keywords

EID: 0000800391     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510351     Document Type: Article

References (8)

1. K. Burrage and P. M. Burrage, High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Appl. Numer. Math., 20 (1996), pp. 1-21.
2. P. M. Burrage, Numerical methods for stochastic differential equations, Ph.D. thesis, Department of Mathematics, University of Queensland, Australia, 1998.
3. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, U.K., 1987.
4. T. C. Gard, Introduction to Stochastic Differential Equations, Marcel Dekker, New York, 1988.
5. P. E. Kloeden and E. Platen, Relations between multiple Itô and Stratonovich integrals, Stochastic Anal. Appl., 9(3) (1991), pp. 311-321.
6. P. E. Kloeden and E. Platen, The Numerical Solution of Stochastic Differential Equations, Springer-Verlag, 1992.
7. G. N. Milstein, E. Platen, and H. Schurz, Balanced implicit methods for stiff stochastic systems, Inst. of Advanced Studies, ANU, Canberra, Australia, 1994.
8. W. Rümelin, Numerical treatment of stochastic differential equations, SIAM J. Numer. Anal., 19 (1982), pp. 604-613.