Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations

BIT Numerical Mathematics

Volumn 37, Issue 1, 1997, Pages 43-66

  Komori, Yoshio ^a   Mitsui, Taketomo ^a   Sugiura, Hiroshi ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Order conditions; Stochastic initial value problem; Stratonovich Taylor expansion; Time discrete approximation; Weak scheme

Indexed keywords

EID: 0642303008     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510172     Document Type: Article

References (14)

1. S. S. Artem'ev, The stability of numerical methods for solving stochastic differential equations, Bulletin of the Novosibirsk Computing Center, 2 (1993).
2. S. S. Artem'ev and I. O. Shukurko, Numerical analysis of dynamics of oscillatory stochastic systems, Soviet J. Numer. Anal. Math. Modelling, 6 (1991), pp. 277-298.
3. T. A. Averina and S. S. Artem'ev, A new family of numerical methods for solving stochastic differential equations, Soviet Math. Dokl., 33 (1986), pp. 736-738.
4. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Runge-Kutta and General Linear Methods, John Wiley & Sons, Chichester, 1987.
5. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Systems, Springer-Verlag, Berlin, 1991.
6. N. Hofmann and E. Platen, Stability of weak numerical schemes for stochastic differential equations, Computers Math. Applic., 28 (1994), pp. 45-57.
7. P. Kaps and P. Rentrop, Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations, Numer. Math., 33 (1979), pp. 55-68.
8. P. Kaps and G. Wanner, A study of Rosenbrock-type methods of high order, Numer. Math., 38 (1981), pp. 279-298.
9. J. R. Klauder and W. P. Petersen, Numerical integration of multiplicative-noise stochastic differential equations, SIAM J. Numer. Anal., 22 (1985), pp. 1153-1166.
10. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992.
11. G. N. Milstein and E. Platen, The integration of stiff stochastic differential equations with stable second moments, Technical Report SRR 014-94, The Australian National University, Canberra 1994.
12. E. Platen. Zur zeitdiskreten Approximation von Itoprozessen, Diss. B, PhD thesis, IMath, Akad. der Wiss. der DDR, 1984.
13. E. Platen, Higher-order weak approximation of Ito diffusions by Markov chains, Probability in the Engineering and Informational Sciences, 6 (1992), pp. 391-408.
14. E. Platen, On weak implicit and predictor-corrector methods, Mathematics and Computers in Simulation, 38 (1995), pp. 69-76.