Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
Standard Bases of Differential Ideals
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Admissible orderings and finiteness criteria for differential standard bases
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Involution and Difference Schemes for the Navier---Stokes Equations
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Notes on triangular sets and triangulation-decomposition algorithms II: differential systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Thomas decomposition of algebraic and differential systems
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra
Journal of Symbolic Computation
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We consider finite difference approximations to systems of polynomially-nonlinear partial differential equations the coefficients of which are rational functions over rationals in the independent variables. The notion of strong consistency which we introduced earlier for linear systems is extended to nonlinear ones. For orthogonal and uniform grids we describe an algorithmic procedure for the verification of the strong consistency based on the computation of difference standard bases. The concepts and algorithmic methods of the present paper are illustrated by two finite difference approximations to the two-dimensional Navier-Stokes equations. One of these approximations is strongly consistent, while the other is not.