Iterative method of analysis for nonlinear singularly perturbed initial and boundary value problems
type: Item
instance of: scholarly article
title: Iterative method of analysis for nonlinear singularly perturbed initial and boundary value problems
zbMATH Open document ID: 1025.34008
author: Yu. A. Konyaev
published in: Russian Mathematics
publication date: 2001-03-07T00:00:00Z
review text: The author obtains results concerning the existence of a unique bounded solution to a class of regular and singularly perturbed nonlinear initial and boundary value problems. An asymptotic decomposition of the solution to singularly perturbed multipoint boundary value problems with weak nonlinearity is done by means of special matrix transformations and an iterative method. It is shown that the solution is valid in the absence of resonance correlations and in the presence of both identical and nonidentical resonances. The new algorithm is convenient for numerical realization. It distinguishes the singularities of the solution in a closed analytic form.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1541449
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary value problem
zbMATH Keywords: iterative method
zbMATH Keywords: existence of a unique solution
zbMATH Keywords: nonlinear differential equations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541449