A new approach to boundary value equations and application to a generalization of Airy's equation
type: Item
instance of: scholarly article
title: A new approach to boundary value equations and application to a generalization of Airy's equation
zbMATH Open document ID: 0678.65057
DOI: 10.1016/0022-247X(89)90083-8
author: G. Adomian
author: M. Elrod
author: Randolph Rach
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: For the boundary value problem: \(u''-kxu=g\), \(u(-1)=u(1)=0\), where k and g are constants, the authors compute a power series solution \(u=\Sigma_ nu_ n\) with the iteration \(u_ 0=c_ 1+c_ 2x+gx^ 2/2,\) \(u''_{n+1}=kxu_ n.\) A similar computation is carried out for the equation \(u''+au=g\) with general linear boundary conditions. The paper concludes stating a similar iteration for the equation \(u_{xx}+au_{yy}=g\) with linear boundary conditions and constant a, g.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 34B30
zbMATH DE Number: 4111934
zbMATH Keywords: Airy's equation
zbMATH Keywords: explicit solution
zbMATH Keywords: power series solution
zbMATH Keywords: iteration
reviewed by: Martin Brokate
MaRDI profile type: Publication
cites work: Variational Methods for Approximating Solutions of $\nabla ^2 u(x) = f(x) + k(x)u(x)$ and Generalizations
cites work: Nonlinear equations with mixed derivatives
cites work: Inversion of nonlinear stochastic operators
cites work: On the solution of partial differential equations with specified boundary conditions
description: scientific article; zbMATH DE number 4111934