Skip to main content
SpringerLink
Log in

Multiplicative Runge–Kutta methods

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Volterra, V., Hostinsky, B.: Operations Infinitesimales Lineares. Herman, Paris (1938).

  • 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).

    Article  MATH  Google Scholar 

  • Kasprzak, W., Lysik, B., Rybaczuk, M.: Measurements, Dimensions, Invariants Models and Fractals. Ukrainian Society on Fracture Mechanics, SPOLOM, Wroclaw-Lviv, Poland (2004).

  • Prosnak, J.: Introduction to Numerical Fluid Mechanics. Approximate Methods of Solving Ordinary Differential Problems (in Polish). Zaklad Narodowy im. Ossolinskich, Wroclaw, Poland (1993).

  • Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester, England (2003).

  • 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).

  • Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos. An Introduction to Dynamical Systems. Springer-Verlag, New York (2000).

  • Aniszewska, D., Rybaczuk, M.: Analysis of the multiplicative Lorenz system. Chaos Solitons Fractals 25, 79–90 (2005).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Materials Science and Applied Mechanics, Wroclaw University of Technology, Smoluchowskiego 25, 50-370, Wroclaw, Poland

    Dorota Aniszewska

Authors
  1. Dorota Aniszewska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dorota Aniszewska.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aniszewska, D. Multiplicative Runge–Kutta methods. Nonlinear Dyn 50, 265–272 (2007). https://doi.org/10.1007/s11071-006-9156-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-006-9156-3

Keywords

Search

Navigation