Construction of Partial Laurent Solutions to Truncated Differential Systems

Abstract

In this paper, we consider the problem of constructing the first terms of formal Laurent series that act as solutions to a given component yk (\(1 \leqslant k \leqslant m\)) of a vector of unknowns y for a differential system \(y{\kern 1pt} ' = Ay\), where \(y = {{({{y}_{1}}, \ldots ,{{y}_{m}})}^{T}}\) and A is an m × m matrix whose elements are d-truncations of formal Laurent series, i.e., their first terms up to the degree \(d \geqslant 0\) inclusive. An algorithm for solving this problem based on the truncated series Laurent solution (TSLS) algorithm is proposed. The first terms of the formal Laurent solutions for yk constructed by the proposed algorithm are invariant to possible continuations of elements of the original system’s matrix.

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Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00032.

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Correspondence to A. A. Panferov.

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Translated by Yu. Kornienko

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Panferov, A.A. Construction of Partial Laurent Solutions to Truncated Differential Systems. Program Comput Soft 47, 34–42 (2021). https://doi.org/10.1134/S0361768821010072

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