Long-Term Dynamics

  • David F. Griffiths
  • Desmond J. Higham
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


There are many applications where one is concerned with the long-term behaviour of nonlinear ODEs. It is therefore of great interest to know whether this behaviour is accurately captured when they are solved by numerical methods.


Bifurcation Diagram Linear Stability Euler Method Logistic Equation Absolute Stability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [5]
    M. Braun. Differential Equations and their Applications. Springer-Verlag, 1983.Google Scholar
  2. [25]
    D. F. Griffiths, P. K. Sweby, and H. C. Yee. On spurious asymptotic numerical solutions of explicit Runge–Kutta methods. IMA J. Num. Anal., 12:319–338, 1992.MATHCrossRefMathSciNetGoogle Scholar
  3. [41]
    C. T. Kelley. Iterative Methods for Linear and Nonlinear Equations, volume 16 of Frontiers in Applied Mathematics. SIAM, Philadelphia, USA, 1995.Google Scholar
  4. [65]
    A. M. Stuart and A. R. Humphries. Dynamical Systems and Numerical Analysis. Cambridge University Press, Cambridge, 1996.MATHGoogle Scholar
  5. [66]
    J. M. T. Thompson and H. B. Stewart. Nonlinear Dynamics and Chaos, Geometrical Methods for Engineers and Scientists. John Wiley and Sons, 2nd edition, 2002.Google Scholar
  6. [68]
    F. Verhulst. Nonlinear Differential Equations and Dynamical Systems. Universitext. Springer-Verlag, 2nd edition, 1990.Google Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Mathematics DivisionUniversity of DundeeDundeeUK
  2. 2.Department of Mathematics and StatisticsUniversity of StrathclydeGlasgowUK

Personalised recommendations