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A Method to Study the Cauchy Problem for a Singularly Perturbed Homogeneous Linear Differential Equation of Arbitrary Order

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Abstract

We construct a sequence converging to the solution to the Cauchy problem for a singularly perturbed linear homogeneous differential equation of any order. This sequence is asymptotic in the following sense: the distance (with respect to the norm of the space of continuous functions) between its nth element and the solution to the problem is proportional to the (n + 1)th power of the perturbation parameter.

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Authors and Affiliations

  1. Moscow State University, Faculty of Physics, Leninskie Gory, Moscow, 119991, Russia

    E. E. Bukzhalev

Authors
  1. E. E. Bukzhalev
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Correspondence to E. E. Bukzhalev.

Additional information

Original Russian Text © E.E. Bukzhalev. 2018. published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika. 2018. Vol. 73, No. 2, pp. 3–12.

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Bukzhalev, E.E. A Method to Study the Cauchy Problem for a Singularly Perturbed Homogeneous Linear Differential Equation of Arbitrary Order. Moscow Univ. Math. Bull. 73, 41–49 (2018). https://doi.org/10.3103/S0027132218020018

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  • DOI: https://doi.org/10.3103/S0027132218020018

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