Department of Mathematics,

University of Patras,

Rio 26500,

GREECE

E-mail: spawn@math.upatras.gr, tsoubeli@math.upatras.gr

_{A new heuristic algorithm for solving overdetermined
systems of PDEs in Mathematica}

**Abstract:**

The outline and the main features of a heuristic algorithm for solving
overdetermined systems of PDEs is decribed. This algorithm, which we call
“Seek&Solve”, is the core element of the command *SolveOverdeterminedEqs*
of the *Mathematica* based symmetry analysis package SYM, developed
by the authors recently. Characteristic examples are presented, showing
the effectiveness of the algorithm - particularly in the case where the
over-determined system admits “singular” solutions corresponding to special
values of the parameters involved.