A method of solving real linear homogeneous second-order differential equations in an infinite interval
type: Item
instance of: scholarly article
title: A method of solving real linear homogeneous second-order differential equations in an infinite interval
zbMATH Open document ID: 0773.65058
author: A. A. Krapivina
published in: Computational Mathematics and Mathematical Physics
publication date: 1993-06-29T00:00:00Z
review text: The author considers an approximate method for the solution of the differential equation \(y''+p(x)y=0\) on the interval \((0,\infty)\). Suppose that the coefficient \(p(x)\) has the limiting value \(p_ 0\) at \(\infty\), and its asymptotic expansion is known as \(x\to\infty\). She gives a systematic way to derive the asymptotic expansion of the solution. The initial idea is to consider the new unknown \(A(x)=Y'(x)/Y(x)\) where, putting \(y_ 1(x)\) and \(y_ 2(x)\) as bounded solutions, \(Y(x)=y_ 1(x)+iy_ 2(x)\). The introduction of the complex-valued function makes the problem harder, but it is claimed the method is more useful. A simple example is given.
reviewed by: Taketomo Mitsui
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 220934
zbMATH Keywords: linear homogeneous second-order differential equations
zbMATH Keywords: numerical example
zbMATH Keywords: infinite interval
zbMATH Keywords: asymptotic expansion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 220934