An adaptive timestepping algorithm for stochastic differential equations

Journal of Computational and Applied Mathematics

Volumn 161, Issue 2, 2003, Pages 417-430

  Lamba, H ^a  

^a GEORGE MASON UNIVERSITY   (United States)

Author keywords

Error control; Numerical integration; Stochastic differential equations

Indexed keywords

ADAPTIVE ALGORITHMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS;

WIENER PROCESS;

RANDOM PROCESSES;

ALGORITHM; EQUATION; STOCHASTIC METHOD;

EID: 0242708960     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.05.001     Document Type: Article

References (22)

1. Artemiev S.S. Averina T.A. Numerical Analysis of systems of ordinary and Stochastic Differential Equations 1997 VSP Utrecht
2. Burrage K. Burrage P.M. High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations Appl. Numer. Math. 22 1-3 1996 81-101
3. P.M. Burrage, Runge-Kutta methods for stochastic differential equations, Ph.D. Thesis, University of Queensland, 1998.
4. Burrage P.M. Burrage K. Mitsui T. Numerical solutions of stochastic differential equations-implementation and stability issues J. Comput. Appl. Math. 125 2000 171-182
5. Butcher J.C. The Numerical Analysis of Ordinary Differential Equations 1992 Wiley New York
6. Gaines J.G. Lyons T.J. Random generation of stochastic area integrals SIAM J. Appl. Math. 54 1994 1132-1146
7. Gaines J.G. Lyons T.J. Variable stepsize control in the numerical solution of stochastic differential equations SIAM J. Appl. Math. 57 1997 1455-1484
8. Gustafsson K. Lundh M. Soderlind G A PI-stepsize control for the numerical solution of ordinary differential equations BIT 28 1988 270-287
9. Hairer E. Nørsett S.P. Wanner G. Solving ordinary differential equations I. Nonstiff problems 2nd Edition 1993 Springer Berlin
10. Hall G. Equilibrium states of Runge-Kutta schemes ACM Trans. Math. Software 11 1985 289-301
11. Hall G. Higham D.J. Analysis of stepsize selection schemes for Runge-Kutta codes IMA J. Numer. Anal. 8 1988 305-310
12. Hoffman N. Muller-Gronbach T. Ritter K. Optimal approximation of stochastic differential equations by adaptive step-size control Math. Comput. 69 2000 1017-1034
13. Kloeden P.E. Platen E. Numerical Solution of Stochastic Differential Equations 1992 Springer Berlin
14. Lamba H. Dynamical systems and adaptive time-stepping in ODE solvers BIT 40 2000 314-335
15. H. Lamba, J. Mattingly, A.M. Stuart, Strong convergence of an adaptive Euler-Maruyama scheme for stochastic differential equations, Technical Report, University of Warwick 2003.
16. Lévy P. Processus Stochastiques et Mouvement Brownien, Monographies des Probabilities 1948 Gauthier-Villars Paris
17. Li C.W. Liu X.Q. Approximation of multiple stochastic integrals and its application to stochastic differential equations Nonlinear Anal. 30 1997 697-708
18. Mauthner S. Stepsize control in the numerical solution of stochastic differential equations J. Comput. Appl. Math. 100 1998 93-109
19. Oksendal B. Stochastic Differential Equations-An Introduction with Applications 1998 Springer Berlin
20. Rößler A. Lehn J. Schein O. Adaptive schemes for the numerical solution of SDEs-a comparison J. Comput. Appl. Math. 138 2002 297-308
21. Shampine L.F. Numerical Solution of Ordinary Differential Equations 1994 Chapman - Hall New York
22. Stuart A.M. Humphries A.R. The essential stability of local error control for dynamical systems SIAM J. Numer. Anal. 32 1995 1940-1971