Numerical solution of stochastic differential problems in the biosciences

Journal of Computational and Applied Mathematics

Volumn 185, Issue 2, 2006, Pages 422-440

  Carletti, M ^a  

^a UNIVERSITY OF URBINO   (Italy)

Author keywords

Biomathematical modelling; Numerical methods for stochastic equations; Stochastic delay differential equations; Stochastic ordinary differential equations

Indexed keywords

CODES (SYMBOLS); MATHEMATICAL MODELS; RANDOM PROCESSES; RUNGE KUTTA METHODS; STOCHASTIC CONTROL SYSTEMS;

BIOMATHEMATICAL MODELING; NUMERICAL METHODS FOR STOCHASTIC EQUATIONS; STOCHASTIC DELAY DIFFERENTIAL EQUATIONS; STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 25144516340     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.03.020     Document Type: Conference Paper

References (18)

1. C.T.H. Baker, E. Buckwar, Introduction to the numerical analysis of stochastic delay differential equations, Numerical Analysis report No. 345 (revised), Manchester Centre for Computational Mathematics, 2000.
2. E. Beretta, M. Carletti, and F. Solimano On the effects of environmental fluctuations in a simple model of bacteria-bacteriophage interaction Canad. Appl. Math. Quart. 8 4 2000 321 366
3. E. Beretta, and Y. Kuang Modeling and analysis of a marine bacteriophage infection Math. Biosci. 149 1998 57 76
4. L. Brugnano, K. Burrage, and P.M. Burrage Adams-type methods for the numerical solution of stochastic ordinary differential equations BIT 40 3 2000 451
5. P.M. Burrage, Runge-Kutta methods for stochastic differential equations, Ph.D. Thesis, University of Queensland, Brisbane, Australia, 1999.
6. K. Burrage, and P.M. Burrage High order explicit Runge-Kutta methods for stochastic ordinary differential equations Appl. Numer. Math. 22 1996 81
7. K. Burrage, and P.M. Burrage Order conditions of stochastic Runge-Kutta methods by B-series SIAM J. Numer. Anal. 38 5 2000 1626
8. K. Burrage, P.M. Burrage, and J.A. Belward A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations BIT 37 1997 771
9. M. Carletti On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment Math. Biosci. 175 2 2002 117 131
10. M. Carletti, Numerical simulation of a Campbell-like stochastic delay model for bacteriophage infection, preprint.
11. M. Carletti, K. Burrage, and P.M. Burrage Numerical simulation of stochastic ordinary differential equations in biomathematical modelling Math. Comput. Simulation 64 2004 271 277
12. D.J. Higham Mean-square and asymptotic stability of the stochastic theta method SIAM J. Numer. Anal. 38 3 2000 753 769
13. D.J. Higham, X. Mao, A.M. Stuart, Strong convergence of numerical methods for nonlinear stochastic differential equations, University of Strathclyde Mathematics Research Report 13, Glasgow, 2001.
14. P.E. Kloeden, and R.A. Pearson The numerical solution of stochastic differential equations J. Austral. Math. Soc. Ser. B 20 1977 8
15. P.E. Kloeden, and E. Platen Numerical Solution of Stochastic Differential Equations 1995 Springer Berlin
16. P.E. Platen, Zur zeitdiskreten Approximation von Itoprozessen, Dissertationen B., IMath, Akademiya der Wissenschaftsgesch der DDR, Berlin, 1984.
17. W. Rümelin Numerical treatment of stochastic differential equations SIAM J. Numer. Anal. 19 1982 604
18. Y. Saito, and T. Mitsui Stability analysis of numerical schemes for stochastic differential equations SIAM J. Numer. Anal. 33 6 1996 2254 2267