Computer Algebra Tools for Handling Ordinary Diierential Equations (cathode 2) Han Sur Lesse Workshop Extended Abstracts Esprit Working Group 24490

A linearization of PDEs based on conservation laws

A method based on innnite parameter conservation laws is described to factor linear differential operators out of nonlinear partial diierential equations (PDEs) or out of diierential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (system) if that is possible. Innnite parameter conservation laws can be computed, for example, with a computer alg...

Integration and Diierential Equations in Computer Algebra

We describe in this paper how the problems of computing indeenite integrals and solving linear ordinary diierential equations in closed form are now solved by computer algebra systems. After a brief review of the mathematical history of those problems, we outline the two major algorithms for them (respectively the Risch and Singer algorithms) and the recent improvements on those algorithms whic...

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

Advanced courses in Macroscopic Physical Chemistry (Han-sur-Lesse winterschool 2005) THEORY OF POLYMER DYNAMICS

Iterated Commutators, Lie's Reduction Method and Ordinary Diierential Equations on Matrix Lie Groups

In the context of devising geometrical integrators that retain qualitative features of the underlying solution, we present a family of numerical methods (the method of iterated commutators, 5, 13]) to integrate ordinary diierential equations that evolve on matrix Lie groups. The schemes apply to the problem of nding a numerical approximation to the solution of Y 0 = A(t;Y)Y; Y (0) = Y0; whereby...