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

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