38 citations · 44 across the 6 of their papers we have counts for
6 papers
Strong Consistency and Thomas Decomposition of Finite Difference Approximations to Systems of Partial Differential Equations
Vladimir P. Gerdt, Daniel Robertz, Yuri A. Blinkov
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…
On Consistency of Finite Difference Approximations to the Navier-Stokes Equations
P. Amodio, Yu. Blinkov, V. Gerdt +1
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these appro…
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
Vladimir P. Gerdt, Yuri A. Blinkov, Vladimir V. Mozzhilkin
In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enla…
Janet Bases of Toric Ideals
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we present a version of the general polynomial involutive algorithm for computing Janet bases specialized to toric ideals. The relevant data structures are Janet tree…
Minimal Involutive Bases
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we present an algorithm for construction of minimal involutive polynomial bases which are Groebner bases of the special form. The most general involutive algorithms a…
Involutive Bases of Polynomial Ideals
Vladimir P. Gerdt, Yuri A. Blinkov
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new con…