Abstract
An asymptotic solution of the linear Cauchy problem in the presence of a “weak” turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explicitly. Estimates are given for ε that characterize the behavior of singularities for ϵ→0. The asymptotic convergence of a regularized series is proven. The results are illustrated by an example. Bibliography: six titles.
Highlights
IntroductionA. Lomov [1] is used to construct a regularized asymptotic solution of a singularly-perturbed inhomogeneous Cauchy problem on the entire interval [0, T] in the presence of a spectral singularity in the form of a “weak” turning point for the limit operator
In this paper, the regularization method of S
We note the paper [2] devoted to the construction of the asymptotic behavior of the solution of singularly-perturbed Cauchy problems for integro-differential equations in the presence of spectral features of the limit operator
Summary
A. Lomov [1] is used to construct a regularized asymptotic solution of a singularly-perturbed inhomogeneous Cauchy problem on the entire interval [0, T] in the presence of a spectral singularity in the form of a “weak” turning point for the limit operator. In presenting the regularization method for solving problem (2), we will use the Lagrange–Sylvester interpolation polynomials, which describe differentiable functions f (t) defined at the point t0 , t1 , ..., tm together with their derivatives.
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