Existence and enclosure results for continua of solutions of parameter- dependent nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Existence and enclosure results for continua of solutions of parameter- dependent nonlinear boundary value problems
zbMATH Open document ID: 0834.65119
DOI: 10.1016/0377-0427(94)00091-E
published in: Journal of Computational and Applied Mathematics
publication date: 1995-10-23T00:00:00Z
review text: The author proposes a numerical method for computing enclosures for continua of solutions of nonlinear elliptic boundary value problems depending upon a real parameter. The method is extended to turning-point problems by change of parameters. The main idea is to combine a previous method already suggested by the author [Computing 49, No. 1, 25-44 (1992; Zbl 0771.65087)] with interpolation techniques and the implicit function theorem in Banach space.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 808370
zbMATH Keywords: continuum of solutions
zbMATH Keywords: enclosures
zbMATH Keywords: nonlinear elliptic boundary value problems
zbMATH Keywords: turning-point problems
author: Michael Plum
reviewed by: Guy Jumarie
describes a project that uses: PITCON
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
cites work: Q3998344
cites work: Q5520389
cites work: Q3763475
cites work: Q3675430
cites work: Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate Method
cites work: Optimale Eigenwerteinschließungen
cites work: A numerical approach to the proof of existence of solutions for elliptic problems II
cites work: Bounds for eigenvalues of second-order elliptic differential operators
cites work: Q3985896
cites work: Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
cites work: Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems
cites work: An Existence and Inclusion Method for Two‐Point Boundary Value Problems with Turning Points
cites work: Q4851732
cites work: Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter
cites work: On the monotone convergence of Newton's method
cites work: Q3734983
cites work: Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points
cites work: Q3706042
description: scientific article; zbMATH DE number 808370