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For a wide class of polynomially nonlinear systems of partial differentialequations we suggest an algorithmic approach that combines differential anddifference algebra to analyze s(trong)-consistency of finite differenceapproximations. Our approach is applicable to regular solution grids. For thegrids of this type we give a new definition of s-consistency for finitedifference approximations which generalizes our definition given earlier forCartesian grids. The algorithmic verification of s-consistency presented in thepaper is based on the use of both differential and difference Thomasdecomposition. First, we apply the differential decomposition to the inputsystem, resulting in a partition of its solution space. Then, to the outputsubsystem that contains a solution of interest we apply a difference analogueof the differential Thomas decomposition which allows to check thes-consistency. For linear and some quasi-linear differential systems one canalso apply difference \Gr bases for the s-consistency analysis. We illustrateour methods and algorithms by a number of examples, which include Navier-Stokesequations for viscous incompressible flow.

Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations