ASYMPTOTICS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH A TURNING POINT
DOI:
https://doi.org/10.52754/16948645_2022_1_4Keywords:
unstable spectrum, V. Vazov's system of equations, turning point, singularly perturbed Cauchy problem, small parameter, boundary functionsAbstract
The article deals with the problem of constructing an asymptotic solution of the initial problem for the inhomogeneous Wolfgang Richard Wasow (25.07.1909-11.09.1993) equation. The inhomogeneous system of equations of V. Vazov belongs to the class of singularly perturbed ordinary differential equations. Features of the problem under study: 1) at the initial point, the main matrix is irreversible; 2) there is a small parameter before the derivative; at points other than the starting point, the main matrix has two elementary divisors of the first degree and one elementary divisor of the second degree at the starting point. In addition, the spectrum of the Vazov equation is unstable. The asymptotic expansion of the formulated problem is constructed by the method of generalized boundary functions.
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