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Characteristic sets for ordinary differential equations

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Abstract

In this paper, the problem of the construction of a characteristic set in the sense of Kolchin for a radical differential ideal is considered. Algorithms for constructing such sets in the ordinary case for arbitrary radical differential ideals, which are based on the estimate of the orders of their elements, are presented. These algorithms are applicable in the case of an orderly ranking on the set of the derivatives. Advantages of the regular and characteristic decompositions of radical differential ideals are discussed.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, 119992, Vorob’evy gory, Moscow, Russia

    M. V. Kondratieva & A. I. Ovchinnikov

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  1. M. V. Kondratieva
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  2. A. I. Ovchinnikov
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Translated from Programmirovanie, Vol. 31, No. 2, 2005.

Original Russian Text Copyright © 2005 by Kondratieva, Ovchinnikov.

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Kondratieva, M.V., Ovchinnikov, A.I. Characteristic sets for ordinary differential equations. Program Comput Soft 31, 91–96 (2005). https://doi.org/10.1007/s11086-005-0019-3

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  • DOI: https://doi.org/10.1007/s11086-005-0019-3

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