NODES

Non linear Ordinary Differential Equations Solver


NODES is a project being developed at the Computer Algebra Department of the Université Libre de Bruxelles. It is part of the European ESPRIT contact group called CATHODE.

Its purpose is the analyse of autonomous non linear first order ordinary differential systems. A matrix formalism (the so-called quasi monomial one) has been introduced by L. Brenig and A. Goriely to represent non linear ODE's. It is similar to the matrix notation introduced for linear systems. It can also be viewed as a multivariate generalisation of the Bernoulli equations. Thanks to that notation, concepts and methods can be formulated using only simple linear algebra. It has been succesfully used to find polynomial first integrals, invariants It has also some tools for bifurcation analysis, normal forms and numerical integration.

The software

NODES has been implemented using the computer algebra system MAPLE. Last version is 2.6 (september 97). You can have a look at
  • a short users manual (also in postscript version)
  • the reference manual (also in postscript version)
  • a demonstration (also in postscript version)
  • the README file (instructions on installation)
    •

    Downloading the software

    You can download
  • NODES 2.6. The last version. Works with Maple V.4
  • NODES 2.5. Works with Maple V.3. Less functionalities
    •

    Related papers (in construction)

  • M. Codutti, NODES : Non linear Ordinary Differential Equations Solver, Proceedings of ISSAC'92 (International Symposium on Symbolic and Algebraic Computation), Berkeley, Jully 1992.

    • Related works

    NODES use a locally developed literate programming system called MapleDoc.

    Codutti Marco
    Last modified: Wed Oct 1 14:23:05 MET DST 1997