Involutive bases of polynomial ideals
Minimal involutive bases
An algorithm for construction of minimal involutive polynomial bases which are Grobner bases of the special form is presented which provides correctness and termination of involutive algorithms for any finite set of input polynomials and any admissible monomial ordering.
Janet-Like Monomial Division
Though Janet-like division is not involutive, it preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity, and is more efficient than its Janet division counterpart.
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
An algorithmic approach to the generation of fully con- servative difference schemes for linear partial differential equations based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives.
Algorithmic Verification of Linearizability for Ordinary Differential Equations
- D. Lyakhov, V. Gerdt, D. Michels
- MathematicsInternational Symposium on Symbolic and Algebraic…
- 13 February 2017
Two algorithms are devised to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables and to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation.
Algorithmic Thomas decomposition of algebraic and differential systems
Algorithmic Approach to Strong Consistency Analysis of Finite Difference Approximations to PDE Systems
- V. Gerdt
- Computer Science, MathematicsInternational Conference on Mathematical Modeling…
- 4 July 2011
A difference analogue of the differential Thomas decomposition and an algorithm for verification of s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation are proposed.
Involutive Division Techniques: Some Generalizations and Optimizations
- V. Gerdt
- 4 December 1999
A new class of involutive divisions induced by certain orderings of monomials is considered. It is proved that these divisions are Noetherian and constructive. Therefore, each of them allows one to…
Involutive Algorithms for Computing
An efficient involutive algorithm based on the concept of involutive monomial division which restricts the conventional division in a certain way and which can be output without any extra computational costs is described.