Gröbner bases and generation of difference schemes for partial differential equations

DOI10.3842/SIGMA.2006.051zbMath1094.68125arXivmath/0605334OpenAlexW2090556056WikidataQ115219740 ScholiaQ115219740MaRDI QIDQ2495207

Yu. A. Blinkov, V. V. Mozzhilkin, Vladimir P. Gerdt

Publication date: 4 July 2006

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605334

zbMATH Keywords

Gröbner basisBurgers equationcomputer algebrapartial differential equationsconservative difference schemesdifference algebraFalkowich-Karman equationJanet-like basislinear difference ideal

Mathematics Subject Classification ID

Related Items (15)

Adaptive and optimal difference operators in image processing ⋮ Involutive method for computing Gröbner bases over \(\mathbb F_2\) ⋮ Investigation of difference schemes for two-dimensional Navier-Stokes equations by using computer algebra algorithms ⋮ The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside ⋮ Discretization of quasilinear evolution equations by computer algebra methods ⋮ Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals ⋮ Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion ⋮ Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier-Stokes equations ⋮ Nonlinear Deformation Waves in a Geometrically and Physically Nonlinear Viscoelastic Cylindrical Shell Containing Viscous Incompressible Fluid and Surrounded by an Elastic Medium ⋮ Optimal Difference Operator Selection ⋮ On the consistency analysis of finite difference approximations ⋮ Algebraic construction of a strongly consistent, permutationally symmetric and conservative difference scheme for 3D steady Stokes flow ⋮ Involution and Difference Schemes for the Navier–Stokes Equations ⋮ Gröbner bases and gradings for partial difference ideals ⋮ A new type of difference dimension polynomials

Uses Software

• Maple
• SINGULAR
• OreModules

This page was built for publication: Gröbner bases and generation of difference schemes for partial differential equations