SYMBOLIC METHODS FOR SYSTEMS OF IMPLICIT ORDINARY DIFFERENTIAL EQUATIONS^*

ABSTRACT

This contribution deals with equivalence problems for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of some normal form, and vice versa. The system is identified with the submanifold in a suitable jet-space, defined by the equations. Therefore, a short introduction to jet theory is presented, as well as its application to systems of differential equations. We present several results for well-determined and under-determined systems and give formulas that describe the transform to an appropriate normal form. Apart from the theoretical results, we give several sketches of computer algebra-based algorithms necessary to solve these problems efficiently.

^*Communicated by J. McPhee.

Acknowledgments

Notes

^*Communicated by J. McPhee.