A geometric index reduction method for implicit systems of differential algebraic equations
Copyright policy )A geometric index reduction method for implicit systems of differential algebraic equations
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (that is, a semi-explicit DAE system of differentiation index 1) in as many variables as the order of the input system. This can be done by means of a Kronecker-type algorithm with bounded complexity.
- CONICET Argentina
- École Polytechnique France
- University of Lille France
- National Scientific and Technical Research Council Argentina
- Universidid De Buenos Aires Argentina
index, Computer Science - Symbolic Computation, FOS: Computer and information sciences, Kronecker algorithm, 68W30, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Implicit systems of Differential Algebraic Equations, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, Jacobi bound, Differentiation Index, implicit ordinary differential equation, MSC 12H05, 12H05, 34A09, 68W30, differential algebraic equation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, https://purl.org/becyt/ford/1.1, https://purl.org/becyt/ford/1, Transformation and reduction of ordinary differential equations and systems, normal forms, geometric resolution, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Algebra and Number Theory, Geometric resolution, DAE systems, Index, Computational Mathematics, Effectivity, complexity and computational aspects of algebraic geometry, Kronecker Algorithm, Mathematics - Classical Analysis and ODEs, 34A09, Geometric Resolution, Dae Systems, Implicit ordinary differential equations, differential-algebraic equations
index, Computer Science - Symbolic Computation, FOS: Computer and information sciences, Kronecker algorithm, 68W30, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Implicit systems of Differential Algebraic Equations, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, Jacobi bound, Differentiation Index, implicit ordinary differential equation, MSC 12H05, 12H05, 34A09, 68W30, differential algebraic equation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, https://purl.org/becyt/ford/1.1, https://purl.org/becyt/ford/1, Transformation and reduction of ordinary differential equations and systems, normal forms, geometric resolution, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Algebra and Number Theory, Geometric resolution, DAE systems, Index, Computational Mathematics, Effectivity, complexity and computational aspects of algebraic geometry, Kronecker Algorithm, Mathematics - Classical Analysis and ODEs, 34A09, Geometric Resolution, Dae Systems, Implicit ordinary differential equations, differential-algebraic equations
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