Some cooking recipes for DE systems
Edgardo Cheb-Terrab, CECM/MITACS
When computing exact solutions to PDE systems, a crucial step is to compute - first of all - what is frequently called a "differential Grobner basis using lexicographical ordering" for it. In simple words this amounts to triangularizing the PDE system, permiting one to solve it by sequentially solving subsets of PDEs involving a single unknown at a time. In many situations, however, before computing a differential Grobner basis, it is possible and convenient to start by eliminating some of the unknowns of the system. In various cases the whole PDE system can be solved without computing any integrability conditions - resulting in a relevant saving e.g. in the presence of nonlinear PDEs. More importantly: in the "current Computer Algebra Systems" framework, even some linear PDE systems can *only* be solved when we start eliminating variables before computing any differential Groebner basis. This talk presents some details of the problem and a new Maple implementation of a mixed strategy, where elimination-in-advance and DGB are both used.