We consider the problem of finding asymptotic solutions to linear singular perturbed differential-algebraic equations with simple turning point and develop a technique for the construction of these asymptotic solutions.
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A. M. Samoilenko and P. F. Samusenko, “Asymptotic integration of singularly perturbed differential algebraic equations with turning points. Part I.” Ukr. Mat. Zh., 72, No. 12, 1669–1681 (2020); English translation: Ukr. Math. J., 72, No. 12, 1928–1943 (2021).
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P. F. Samusenko, Asymptotic Integration of Singularly Perturbed Systems of Functional-Differential Equations with Degenerations [in Ukrainian], Vyd. Drahomanov National Pedagogic University, Kyiv (2011).
W. Wasow, Linear Turning Point Theory, Springer, New York (1985).
A. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973).
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A. M. Samoilenko is deceased
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 6, pp. 849–864, June, 2021. Ukrainian DOI: 10.37863/umzh.v73i6.6260.
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Samoilenko, A.M., Samusenko, P.F. Asymptotic Integration of Singularly Perturbed Differential Algebraic Equations with Turning Points. Part II. Ukr Math J 73, 988–1007 (2021). https://doi.org/10.1007/s11253-021-01972-5
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DOI: https://doi.org/10.1007/s11253-021-01972-5