On decomposition of algebraic PDE systems into simple subsystems

DOI10.1007/s10440-008-9202-xzbMath1154.68111OpenAlexW2120706034MaRDI QIDQ941643

Vladimir P. Gerdt

Publication date: 2 September 2008

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-008-9202-x

zbMATH Keywords

Gröbner basisinvolutionPDEsdecomposition algorithmalgebraically simple systemThomas splitting method

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Geometric theory, characteristics, transformations in context of PDEs (35A30) Commutative rings of differential operators and their modules (13N10) Differential algebra (12H05)

Related Items (11)

Singularities of algebraic differential equations ⋮ The Maple package TDDS for computing Thomas decompositions of systems of nonlinear PDEs ⋮ Algorithmic Thomas decomposition of algebraic and differential systems ⋮ Thomas Decomposition and Nonlinear Control Systems ⋮ Algebraically simple involutive differential systems and the Cauchy problem ⋮ Term-ordering free involutive bases ⋮ Thomas Decomposition of Algebraic and Differential Systems ⋮ An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations ⋮ On the algorithmic linearizability of nonlinear ordinary differential equations ⋮ A logic based approach to finding real singularities of implicit ordinary differential equations ⋮ On the consistency analysis of finite difference approximations

Uses Software

• Epsilon

Cites Work

• Spencer \(\delta\)-cohomology, restrictions, characteristics and involutive symbolic PDEs
• Involutive bases of polynomial ideals
• An efficient algebraic algorithm for the geometric completion to involution
• An algorithm for the computation of the radical of an ideal
• On E. Cartan's Prolongation Theorem of Exterior Differential Systems
• Comprehensive Triangular Decomposition
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