  For a wide class of polynomially nonlinear systems of partial differential
equations we suggest an algorithmic approach that combines differential and
difference algebra to analyze s(trong)-consistency of finite difference
approximations. Our approach is applicable to regular solution grids. For the
grids of this type we give a new definition of s-consistency for finite
difference approximations which generalizes our definition given earlier for
Cartesian grids. The algorithmic verification of s-consistency presented in the
paper is based on the use of both differential and difference Thomas
decomposition. First, we apply the differential decomposition to the input
system, resulting in a partition of its solution space. Then, to the output
subsystem that contains a solution of interest we apply a difference analogue
of the differential Thomas decomposition which allows to check the
s-consistency. For linear and some quasi-linear differential systems one can
also apply difference \Gr bases for the s-consistency analysis. We illustrate
our methods and algorithms by a number of examples, which include Navier-Stokes
equations for viscous incompressible flow.
