Existence of multiple solutions for finite difference approximations to second-order boundary value problems
type: Item
instance of: scholarly article
title: Existence of multiple solutions for finite difference approximations to second-order boundary value problems
zbMATH Open document ID: 1019.65054
DOI: 10.1016/S0362-546X(02)00297-3
author: Bevan Thompson
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-28T00:00:00Z
review text: This paper deals with the two-point boundary value problem \[ D^2 y_{k+1}= f(kh, y_k, Dy_k),\quad k= 1,\dots, n-1, \] \[ 0= G((y_0, y_n); (Dy_1, Dy_n)),\;Dy_k= (y_k- y_{k-1})/h,\quad h= 1/n, \] which arises as a finite difference approximation to the problem \[ y''= f(x,y,y'),\quad x\in [0,1],\quad 0= G((y(0), y(1)); (y'(0), y'(1))). \] The author extends results of \textit{R. P. Agarwal}, \textit{H. B. Thompson} and \textit{C. C. Tisdell} [On the existence of multiple solutions to boundary vaule problems for second-order ordinary differential equations (submitted for publications)] and shows that solutions of the discrete problem approximate the solutions of the continuous problem for sufficiently small grid size. Theoretical results are demostrated on certain chemical reactions in tubular reactors.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 80M20
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 1901882
zbMATH Keywords: multiple solutions
zbMATH Keywords: finite difference
zbMATH Keywords: Brouwer degree
zbMATH Keywords: discrete two-point boundary value problems
zbMATH Keywords: discrete lower solutions
zbMATH Keywords: discrete upper solutions
zbMATH Keywords: chemical reactions
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00297-3
OpenAlex ID: W2115993145
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description: scientific article; zbMATH DE number 1901882