Nonlinear Dynamics

, Volume 50, Issue 1–2, pp 265–272 | Cite as

Multiplicative Runge–Kutta methods

  • Dorota Aniszewska
Original Paper


Numerical multiplicative algorithm of Runge–Kutta type for solving multiplicative differential equations is presented. The multiplicative Rössler system has been briefly examined to test the method proposed.


Multiplicative calculus Numerical Runge–Kutta methods Rossler system 


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  1. Volterra, V., Hostinsky, B.: Operations Infinitesimales Lineares. Herman, Paris (1938).Google Scholar
  2. Rybaczuk, M., Kedzia, A., Zielinski, W.: The concept of physical and fractal dimension II. The differential calculus in dimensional spaces. Chaos Solitons Fractals 12, 2537–2552 (2001).zbMATHCrossRefGoogle Scholar
  3. Kasprzak, W., Lysik, B., Rybaczuk, M.: Measurements, Dimensions, Invariants Models and Fractals. Ukrainian Society on Fracture Mechanics, SPOLOM, Wroclaw-Lviv, Poland (2004).Google Scholar
  4. Prosnak, J.: Introduction to Numerical Fluid Mechanics. Approximate Methods of Solving Ordinary Differential Problems (in Polish). Zaklad Narodowy im. Ossolinskich, Wroclaw, Poland (1993).Google Scholar
  5. Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester, England (2003).Google Scholar
  6. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C; The Art of Scientific Computing. Cambridge University Press, Cambridge, MA (1992).Google Scholar
  7. Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos. An Introduction to Dynamical Systems. Springer-Verlag, New York (2000).Google Scholar
  8. Aniszewska, D., Rybaczuk, M.: Analysis of the multiplicative Lorenz system. Chaos Solitons Fractals 25, 79–90 (2005).zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Institute of Materials Science and Applied MechanicsWroclaw University of TechnologyWroclawPoland

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