Adams-type methods for the numerical solution of stochastic ordinary differential equations

BIT Numerical Mathematics

Volumn 40, Issue 3, 2000, Pages 451-470

  Brugnano, L ^a   Burrage, K ^b   Burrage, P M ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Adams methods; Linear multistep formulae; Predictor corrector methods; Stochastic ODEs; Strong convergence

Indexed keywords

EID: 0042185152     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022363612387     Document Type: Article

References (11)

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. K. Burrage and P. M. Burrage, General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equations systems, Appl. Numer. Math., 28 (1998), pp. 161-177.
3. K. Burrage and P. M. Burrage, High strong order methods for non-commutative stochastic ordinary differential equations systems and the Magnus formula, Physica D 133, special issue on Quantifying Uncertainty, (1999), pp. 34-48.
4. K. Burrage and P. M. Burrage, Order conditions of stochastic Runge-Kutta methods by B-series, submitted to SIAM J. Numer. Anal.
5. K. Burrage, P. M. Burrage, and J. Belward, A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations, BIT, 37 (1997), pp. 771-780.
6. K. Burrage and E. Platen. Runge-Kutta methods for stochastic differential equations, Annals of Numer. Math., 1 (1994), pp. 63-78.
7. P. M. Burrage, Numerical Methods for Stochastic Differential Equations, Ph.D Thesis, Department of Mathematics, University of Queensland, Australia, 1998.
8. T. C. Gard, Introduction to Stochastic Differential Equations, Marcel Dekker New York, 1988.
9. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992.
10. P. Sagirov, Stochastic methods in the dynamics of satellites, CISM Lecture Notes 57, Udine, 1970.
11. K. Sobczyk. Stochastic Differential Equations, Kluwer, Dordrecht, 1988.