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Symbolic Investigation of Eigenvectors for General Solution of a System of ODEs with a Symbolic Coefficient Matrix

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Abstract

This paper investigates the problem of symbolic representation for the general solution of a system of ordinary differential equations (ODEs) with symbolically defined constant coefficients in the case where some symbolic constants can vanish. In addition, the symbolic representation of eigenvectors for the system’s coefficient matrix is not unique. It is shown that standard procedures of computer algebra systems search for specific symbolic representations of eigenvectors while ignoring the other symbolic representations. In turn, the eigenvectors found by a computer algebra system can be inadequate for constructing numerical algorithms based on them, which is demonstrated by an example. We propose an algorithm for finding various symbolic representations of eigenvectors for symbolically defined matrices. This paper considers a particular system of ODEs obtained by investigating some solutions of Maxwell’s equations; however, the proposed algorithm can be applied to an arbitrary system with a normal matrix of coefficients.

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Funding

This work was supported by the Russian Science Foundation (grant no. 20-11-20257).

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198, Moscow, Moscow Region, Russian Federation

    D. V. Divakov & A. A. Tiutiunnik

  2. Joint Institute for Nuclear Research, 6, Joliot-Curie str., 141980, Dubna, Russian Federation

    D. V. Divakov

Authors
  1. D. V. Divakov
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  2. A. A. Tiutiunnik
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Correspondence to D. V. Divakov or A. A. Tiutiunnik.

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Translated by Yu. Kornienko

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Divakov, D.V., Tiutiunnik, A.A. Symbolic Investigation of Eigenvectors for General Solution of a System of ODEs with a Symbolic Coefficient Matrix. Program Comput Soft 47, 6–16 (2021). https://doi.org/10.1134/S0361768821010035

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  • DOI: https://doi.org/10.1134/S0361768821010035

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