Computer Algebra and Differential Equations

ISBN-13: 9780521447577 / Angielski / Miękka / 1994 / 268 str.

Evelyne Tournier; Jean-Pierre Ramis

Opis

The Computer Algebra and Differential Equations meeting held in France in June 1992 (CADE-92) was the third of a series of biennial workshops devoted to recent developments in computer algebra systems. This book contains selected papers from the meeting. Three main topics are discussed. The first of these is the theory of D-Modules. This offers an excellent way to handle linear systems of partial differential equations effectively. The second topic concerns the theoretical aspects of dynamical systems, with an introduction to Ecalle theory and perturbation analysis applied to differential equations and other nonlinear systems. The final topic is the theory of normal forms. Here recent improvements in the theory and computation of normal forms are discussed.

Spis treści

1. Motivation and introduction to the theory of D-modules B. Malgrange; 2. D-modules, an overview towards effectivity Ph. Maisonobe; 3. Introduction to the Ecalle theory E. Delabaere; 4. Perturbation analysis of linear systems K. R. Meyer; 5. Normal forms of differential systems J. Della Dora and L. Stolovitch; 6. Versal normal form computation and representation theory J. A. Sanders; 7. Painlevé analysis and normal forms L. Brenig and A. Goriely; 8. Normal forms and Stokes multipliers of nonlinear meromorphic differential equations Y. Sibuya.