Computer Algebra Tools for Handling Ordinary Differential Equations


CATHODE - 7213

Work Area: Symbolic Computation

Keywords computer algebra, ordinary differential equations, integrated set of tools


Start Date: 1 September 92 / Duration: 36 months / Status: running

[ participants / contact ]


Abstract CATHODE is studying the specification of fundamental descriptions of solutions of equations and primitive functions to develop, for the first time, an integrated set of tools, using computer algebra, for handling ordinary differential equations.


Aims

The objectives of the CATHODE Working Group are the study of the specification of a fundamental description of solutions of differential equations and the development, for the first time, of an integrated set of tools for handling ordinary differential equations (including a large library of programs) using computer algebra.

The eventual aim of the partners is to develop computer algebra software that accepts a single ordinary differential equation or a system of such equations, and returns all analytic and quantitative information on its solutions which is available, utilising the complete existing literature of the last two centuries.

Within this framework, a number of particular topics will be studied and new methods developed, in the areas of: the closed form solution of single linear and non-linear equations; the normal forms of systems of linear and non-linear equations; methods for studying bifurcation and other qualitative properties; the equivalance of apparently different equations and systems under transfrmations of variables; numerical evaluation; and graphical representation of the solutions.

Activities

The central activities of the group will be a series of workshops. These will be of two main types: the CADE series, open to a wider audience and presenting the latest developments in the theory and algorithms for differential equations; and a series of internal meetings aimed at the development of the specifications of solutions and algorithms. In association with the internal workshops, a series of 1 or 2 day meetings for contacts in industry and academic research will be organised. The aim of these meetings is not only to disseminate our results but also to clarify which of our lines of development offers the most immediate benefit to practical users. To advance work on specific topics within the main theme, a programme of short visits between group members will also be organised.

The results of our workshops will be published in the CADE proceedings and as a series of technical reports, and programs will be disseminated by electronic transfer. Work on individual topics will appear as research papers. We will maintain contacts with the ESPRIT projects ALCOM, POSSO and NEURON by interchange of visits to workshops and meetings.

Progress and Results

The international workshop CADE-92 has been organised in June 92 at the CIRM in Luminy, Marseille, with the American community. A book containing the main lectures is in press with Cambridge University Press.

The first one week workshop has been organised at Han sur Lesse in Belgium with a one day industry contact involving lectures about industrial Differential equations problems.

The next technical workshop is to be held at Dagstuhl in September 93, at which tangible specifications will be produced.

Potential

The long-term all-inclusive objective of this work is to provide a computerised toolkit (CATHODE) for analytically studying ordinary differential equations that scientists and engineers throughout industry and academia would use on their workstations as a complement to or instead of the numerical solvers and simulators currently running on supercomputers. The activities of the group will provide an essential basis for such a development.

We believe this software could be exploited in the wide range of applications fields in which modelling and simulation by differential equations is used, for example, analysis of algorithmic complexity, non-linear circuit theory, non-linear optics, chemical kinetics, wave propagation, ecological processes, economics and traffic flow.

Latest Publications

Further information about CATHODE is available from the CATHODE home page <URL:http://www-lmc.imag.fr/CATHODE/>.


Coordinator

Université Joseph Fourier - F
Institut IMAG
Laboratoire LMC
BP 53X
F - 38041 Grenoble Cedex

Participants

Université Libre de Bruxelles - B
Swiss Federal Institute of Technology - CH
Gesellschaft für Mathematik und Datenverarbeitung - D
Katholieke Universiteit Nijmegen - NL
Queen Mary and Westfield College - UK

CONTACT POINT

Prof. E. Tournier
tel +33/76 514583
fax +33/76 631263
e-mail: tournier@imag.fr


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CATHODE - 7213, August 1994


please address enquiries to the ESPRIT Information Desk

html version of synopsis by Nick Cook