High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

Applied Numerical Mathematics

Volumn 22, Issue 1-3 SPEC. ISS., 1996, Pages 81-101

  Burrage, K ^a   Burrage, P M ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

STOCHASTIC DIFFERENTIAL EQUATIONS (SDES); STOCHASTIC RUNGE KUTTA METHODS;

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; RANDOM PROCESSES;

NUMERICAL METHODS;

EID: 0030286423     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0168-9274(96)00027-x     Document Type: Article

References (20)

1. K. Burrage and E. Platen, Runge-Kutta methods for stochastic differential equations, Ann. Numer. Math. 1 (1-4) (1994) 63-78.
2. P.M. Burrage, Numerical methods for stochastic differential equations, Ph.D. Thesis, Department of Mathematics, University Queensland, Australia (1997).
3. J.C. Butcher, Coefficients for the study of Runge-Kutta integration processes, J. Austral. Math. Soc. 3 (1963) 185-201.
4. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, London, 1987).
5. C.C. Chang, Numerical solution of stochastic differential equations with constant diffusion coefficients, Math. Comp. 49 (1987) 523-542.
6. T.C. Gard, Introduction to Stochastic Differential Equations (Marcel Dekker, New York, 1988).
7. S. Gill, A process for the step-by-step integration of differential equations in an automatic digital computing machine, Proc. Cambridge Philos. Soc. 47 (1951) 96-108.
8. A. Huťa, Une amélioration de la méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premier ordre, Acta Math. Univ. Comenian. 1 (1956) 201-224.
9. P.E. Kloeden and E. Platen, Stratonovich and Ito Taylor expansions, Math. Nachr. 151 (1991) 33-50.
10. P.E. Kloeden and E. Platen, The Numerical Solution of Stochastic Differential Equations (Springer, 1992).
11. Y. Komori, H. Sugiura and T. Mitsui, Rooted tree analysis of the order conditions of ROW-type schemes for stochastic differential equations, Report No. 7, Mathematical Sciences, Nagoya University, Nagoya, Japan (1994).
12. W. Kutta, Beitrag zür näherungsweisen Integration totaler Differentialgleichungen, Z. Math. Phys. 46 (1901) 435-453.
13. G. Maruyama, Continuous Markov processes and stochastic equations, Rend. Circ. Mat. Palermo 4 (1955) 48-90.
14. R.H. Merson, An operational method for the study of integration processes, in: Proceedings Symposium on Data Processing, Weapons Research Establishment, Salisbury, Australia (1957).
15. G.N. Milstein, A method of second-order accuracy integration of stochastic differential equations, Theor. Probab. Appl. 23 (1978) 396-401.
16. E. Platen, Zur zeitdiskreten Approximation von Itoprozessen, Diss. B., IMath, Akademie der Wissenschaften der DDR, Berlin (1984).
17. E. Platen and W. Wagner, On a Taylor formula for a class of Ito processes, Probab. Math. Statist. 3 (1982) 37-51.
18. W. Rümelin, Numerical treatment of stochastic differential equations, SIAM J. Numer. Anal 19 (1982) 604-613.
19. C. Runge, Über die numerische Auflösung von Differentialgleichungen, Math. Ann. 46 (1895) 167-178.
20. W. Wagner and E. Platen, Approximation of Ito integral equations, Preprint ZIMM, Akademie der Wissenschaften der DDR, Berlin (1978).