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Index reduction of differential algebraic equations by differential Dixon resultant

Author

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  • Qin, Xiaolin
  • Yang, Lu
  • Feng, Yong
  • Bachmann, Bernhard
  • Fritzson, Peter

Abstract

High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish the notion of differential Dixon resultant, which can provide the differential resultant of the enlarged system of original equations. To make use of structure of DAEs, variable pencil technique is given to determine the termination of differentiation. Moreover, we also provide a heuristic method for removing the extraneous factors from differential resultant. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.

Suggested Citation

  • Qin, Xiaolin & Yang, Lu & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2018. "Index reduction of differential algebraic equations by differential Dixon resultant," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 189-202.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:189-202
    DOI: 10.1016/j.amc.2017.12.029
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    References listed on IDEAS

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    1. Qin, Xiaolin & Tang, Juan & Feng, Yong & Bachmann, Bernhard & Fritzson, Peter, 2016. "Efficient index reduction algorithm for large scale systems of differential algebraic equations," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 10-22.
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    Cited by:

    1. Juan Tang & Yongsheng Rao, 2020. "A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations," Mathematics, MDPI, vol. 8(11), pages 1-15, November.

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