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

Divakov, D. V.; Tyutyunnik, A. A.

doi:10.1134/s0361768821010035

Cited by 4 publications

(1 citation statement)

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“…Using of the computer algebra systems for solving systems of differential equations or investigating properties of solutions by the means of symbolic computations is a very popular and fruitful approach [3,4]. One of the problems solved this way is symbolic research on eigenvalues and eigenvectors of matrices, associated with solutions of systems [1,2]. In the present work we investigate eigenvalues of matrices defining asymptotics of a solution to a specific system of differential equations by the means of Wolfram Mathematica.…”

Section: Introductionmentioning

confidence: 99%

Computational aspects of finding a solution asymptotics for a singularly perturbed system of differential equations

Krasikov¹,

Nesterov²

2021

Preprint

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We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We prove a theorem that establishes a relationship between the degree of degeneracy and the numbers of equations in the system and spatial variables in some particular cases. The work hardly depends on the calculation of the eigenvalues of matrices that determine the spatial structure of the asymptotics by the means of computer algebra system Wolfram Mathematica. We put forward a hypothesis on the existence of the found connection for an arbitrary number of equations and spatial variables.

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