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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2016 Volume 22, Number 1, Pages 271–281 (Mi timm1280)

This article is cited in 8 papers

Asymptotic expansion for a solution of an ordinary second-order differential equation with three turning points

D. A. Tursunov

Urals State Pedagogical University, Ekaterinburg

Abstract: Using the generalized method of boundary functions, we construct a uniform asymptotic expansion of the solution of the Dirichlet problem for a singularly perturbed linear inhomogeneous ordinary second-order differential equation with three turning points on the real axis. The constructed asymptotic series is a Puiseux series.

Keywords: asymptotic expansion, turning point, singular (bisingular) perturbation, ordinary second-order differential equation, Airy equation, modified Bessel functions, Dirichlet problem, generalized boundary function, small parameter.

UDC: 517.928

Received: 07.04.2015



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