Maple for Stochastic Differential Equations

  • S. Cyganowski
  • L. Grüne
  • P. E. Kloeden
Part of the Universitext book series (UTX)

Abstract

This chapter introduces the maple software package stochastic consisting of maple routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines. A website address is given from which the software can be downloaded and where up to date information about installment, new developments and literature can be found.

Keywords

Covariance Dinates Tempo 

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References

  1. 1.
    L. Arnold, Stochastic Differential Equations. Wiley, New York, 1974.MATHGoogle Scholar
  2. 2.
    S.S. Artemiev and T.A. Averina, Numerical Analysis of Systems of Ordinary and of Stochastic Differential Equations. VSP, Utrecht, 1997.MATHCrossRefGoogle Scholar
  3. 3.
    R.E. Crandall, Topics in Advanced Scientific Computation, Springer-Verlag, Heidelberg, 1996.MATHCrossRefGoogle Scholar
  4. 4.
    S.O. Cyganowski, Solving Stochastic Differential Equations with Maple, Maple-Tech Newsletter 3 (2) (1996), 38–40.Google Scholar
  5. 5.
    S.O. Cyganowski, A MAPLE Package for stochastic differential equations, in “Computational Techniques and Applications: CTAC95” (Editors A. Easton, and R. May ), World Scientific Publishers, Singapore, 1996, 223–230.Google Scholar
  6. 6.
    S. Cyganowski and P.E. Kloeden, Stochastic stability examined through MAPLE, in Proc. 15th IMACS World Congress, Volume 1: Computational Mathematics (Editor: A. Sydow), Wissenschaft and Technik Verlag, Berlin, 1997, 437–432.Google Scholar
  7. 7.
    S. Cyganowski, P.E. Kloeden and J. Ombach, From Elementary Probability to Stochastic DEs with MAPLE, Springer-Verlag, Heidelberg, 2001.Google Scholar
  8. 8.
    S. Cyganowski, P.E. Kloeden and T. Pohl, MAPLE for stochastic differential equations WIAS Berlin, Preprint Nr. 453, 1998. Availability: Postscript 467 KB,http://www.wias-berlin.de/publications/preprints/453
  9. 9.
    T. Gard, Introduction to Stochastic Differential Equations, Marcel-Dekker, New York, 1988.MATHGoogle Scholar
  10. 10.
    W. Gander and J. Hrebicek, Solving Problems in Scientific Computing using Maple and Matlab, Second Edition, Springer- Verlag, Heidelberg, 1995.MATHCrossRefGoogle Scholar
  11. 11.
    W.S. Kendall, Computer algebra and stochastic calculus, Notices Amer. Math. Soc 37 (1990), 1254–1256.Google Scholar
  12. 12.
    P.E. Kloeden, Stochastic differential equations in environmental modelling and their numerical solution, in Stochastic and Statistical Modelling with Groundwater and Surface Water Applications, (Editor: K. Hipel ), Kluwer Academic Publ., Dordrecht, 1994, 21–32.Google Scholar
  13. 13.
    P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations Springer-Verlag, Heidelberg, 1992; second revised printing 1999.Google Scholar
  14. 14.
    P.E. Kloeden and E. Platen, A survey of numerical methods for stochastic differential equations, J. Stoch. Hydrol. Hydraul 3 (1989), 155–178.MATHCrossRefGoogle Scholar
  15. 15.
    P.E. Kloeden and E. Platen, Numerical methods for stochastic differential equations, in Stochastic Modelling and Nonlinear Dynamics: Applications to Mechanical Systems, (Editor: W. Kliemann ), CRC Press, 1994, S. 437–461.Google Scholar
  16. 16.
    P.E. Kloeden, E. Platen and H. Schurz, Numerical Solution of Stochastic Differential Equations through Computer Experiments, Springer-Verlag, Heidelberg, 1993.Google Scholar
  17. 17.
    P.E. Kloeden, E. Platen and H. Schurz, The numerical solution of nonlinear stochastic dynamical systems: a brief introduction, J. Bifurcation 6 Chaos 1 (1991), 277–286.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    P.E. Kloeden and W.D. Scott, Construction of Stochastic Numerical Schemes through Maple, MapleTech Newsletter 10 (1993), 60–65.Google Scholar
  19. 19.
    G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer, Dordrecht, 1995.Google Scholar
  20. 20.
    G.G. Milstein and M.V. Tret’yakov, Numerical Solution of Differential Equations with Coloured Noise, J. Stat. Physics, 77 (1994) 691–715.CrossRefGoogle Scholar
  21. 21.
    E. Platen, Numerical methods for stochastic differential equations, Acta Numerica, (1999) 197–246.Google Scholar
  22. 22.
    E. Valkeila, Computer algebra and stochastic analysis, some possibilities, CWI Quarterly 4 (1991), 229–238.MathSciNetMATHGoogle Scholar
  23. 23.
    Xu Kedai, Stochastic pitchfork bifurcation: numerical simulations and symbolic calculations using MAPLE, Mathematics and Computers in Simulation 38 (1995), 199–207.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • S. Cyganowski
    • 1
  • L. Grüne
    • 2
  • P. E. Kloeden
    • 2
  1. 1.Tipperary InstituteCo. TipperaryClonmelIreland
  2. 2.Fachbereich MathematikJohann Wolfgang Goethe-UniversitätFrankfurt am MainGermany

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