_{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.