Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implicit Method for Degenerated Differential-Algebraic Equations and
  Applications   Systems of differential-algebraic equations are routinely automatically
produced by modeling enviroments such as Maplesim, System Modeler and Modelica.
Structural methods are important for reducing the index and obtaining hidden
constraints of such daes. This is especially the case for high index non-linear
daes. Although such structural analysis is often successful for many dynamic
systems, it may fail if the resulting Jacobian is still singular due to
symbolic cancellation or numerical degeneration. Existing modified structural
methods can handle some cases caused by symbolic cancellation, where assumes
the determinant of a Jacobian matrix is identically zero. This paper removes
such assumptions and provides numerical methods to analyze such degenerated
cases using real algebraic geometry for polynomially nonlinear daes. Firstly,
we provide a witness point method, which produces witness points on all
components and can help to detect degeneration on all components of
polynomially daes. Secondly, we propose an implicit index reduction method
which can restore a full rank Jacobian matrix for degenerated dae. Thirdly,
based on IIR, we introduce an improved structural method, which can numerically
solve degenerated daes on all components. Examples are given to illustrate our
methods and show their advantages for degenerated daes.

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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat