Abstract
We propose an algorithm for the reduction of a singularly perturbed system of differential equations whose characteristic equation has multiple roots to a system with simple roots.
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REFERENCES
N. I. Shkil', On Asymptotic Methods in the Theory of Linear Differential Equations and Their Applications [in Russian], KSU, Kiev (1996, 1997).
N. N. Moiseev, “Asymptotic representation of solutions of linear differential equations in the case of multiple elementary divisors,” Dokl. Akad. Nauk SSSR, 170, No. 4, 37–43 (1966).
V. K. Grigorenko, On Asymptotic Decomposition of Solutions of Systems of Linear Differential Equations [in Russian], Author's Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Kiev (1972).
G. S. Zhukova, Asymptotic Integration of Linear Ordinary Differential Equations [in Russian], Voronezh University, Voronezh (1988).
A. M. Samoilenko, M. I. Shkil', and V. P. Yakovets', Linear Systems of Differential Equations with Degeneracies [in Ukrainian], Vyshcha Shkola, Kiev (2000).
H. Poincaré, “Sur les équations de la physique et mathématique,” Rend. Pal., 10–11, 57–156 (1894).
H. L. Turritin, “Asymptotic expansions of solutions of systems of ordinary linear differential equations containing a parameter,” Mathematika, 1, No. 2, 29–59 (1957).
N. I. Shkil', I. I. Starun, and V. P. Yakovets, Asymptotic Integration of Linear Systems of Differential Equations with Degeneracies [in Russian], Vyshcha Shkola, Kiev (1991).
N. I. Shkil', “On periodic solutions of systems of second-order differential equations,” Arch. Math. (Brno), 23, No. 1, 53–62 (1987).
N. I. Shkil', “On asymptotic decomposition of solutions of systems of differential equations in the case where the characteristic equation has multiple roots,” Nelin. Kolyv., 3, No. 2, 285–289 (2000).
J. K. Hale, Oscillations in Nonlinear Systems, McGraw-Hill, New York (1963).
I. M. Rapoport, On Some Asymptotic Methods in the Theory of Differential Equations [in Russian], Ukrainian Academy of Sciences, Kiev (1954).
S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko, Asymptotic Methods in the Theory of Linear Differential Equations [in Russian], Naukova Dumka, Kiev (1966).
M. I. Shkil', Asymptotic Methods in Differential Equations [in Ukrainian], Vyshcha Shkola, Kiev (1971).
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Shkil', M.I. On Asymptotic Decomposition of Solutions of Systems of Differential Equations with Slowly Varying Coefficients. Nonlinear Oscillations 5, 546–556 (2002). https://doi.org/10.1023/A:1022898423004
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DOI: https://doi.org/10.1023/A:1022898423004