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We develop a method for evaluation of A. Einstein's strength of systems ofpartial differential and difference equations based on the computation ofHilbert-type dimension polynomials of the associated differential anddifference field extensions. Also we present algorithms for such computations,which are based on the Gr\"obner basis method adjusted for the modules overrings of differential, difference and inversive difference operators. Thedeveloped technique is applied to some fundamental systems of PDEs ofmathematical physics such as the diffusion equation, Maxwell equations andequations for an electromagnetic field given by its potential. In each of thesecases we determine the strength of the original system of PDEs and the strengthof the corresponding systems of partial difference equations obtained byforward and symmetric difference schemes. In particular, we obtain a method forcomparing two difference schemes from the point of view of their strength.

Computation of the Strength of PDEs of Mathematical Physics and their Difference Approximations