Singular Perturbation Theory for Systems of Differential Equations in the Case of Multiple Spectrum of the Limit Operator. Iii

Eliseev, A. G.

doi:10.1070/im1985v025n03abeh001300

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Formalism Of Regularization Methods1

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2019

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“…where ϕ i (t) is a smooth function (in the general case, complex) of a real variable t. To solve linear homogeneous equations, such singularities have been described by Liouville [5][6][7][8].…”

Section: Formalism Of Regularization Methodsmentioning

confidence: 99%

Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

Eliseev

Ratnikova

2019

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By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, the problem with a ”simple” turning point was considered, i.e., one eigenvalue vanishes for t = 0 and has the form t m / n a ( t ) (limit operator is discretely irreversible). The regularization method allows us to construct an asymptotic solution that is uniform over the entire segment [ 0 , T ] , and under additional conditions on the parameters of the singularly perturbed problem and its right-hand side, the exact solution.

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Section: Formalism Of Regularization Methodsmentioning

confidence: 99%