An abstract framework in the numerical solution of boundary value problems for neutral functional differential equations
type: Item
instance of: scholarly article
title: An abstract framework in the numerical solution of boundary value problems for neutral functional differential equations
zbMATH Open document ID: 1348.65104
author: S. Maset
published in: Numerische Mathematik
publication date: 2016-07-14T00:00:00Z
review text: The boundary value problem for functional differential equation of the form \[ y^{\prime}(t) = F(t,y,y^{\prime},p),\qquad t\in [a,b], \] \[ B( y,y^{\prime},p )=0 \] is presented in the abstract form \[ y^{\prime} = \mathbf{F} ( y,y^{\prime},p) \] in an abstract Banach space \(\mathbf{U}\). Using the process of discretization, this form is reduced to a problem of a fixed point in a finite-dimensional space. The convergence of the solutions of this problem to the exact solution is proved, imposing several supplementary conditions on the data of the problem. Numerical illustration of the results is absent.
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 6603365
zbMATH Keywords: functional differential boundary value problem
zbMATH Keywords: discretization in abstract Banach spaces
zbMATH Keywords: convergence
describes a project that uses: PDDE-CONT
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s00211-015-0754-1
OpenAlex ID: W1783677089
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DOI: 10.1007/S00211-015-0754-1
description: scientific article; zbMATH DE number 6603365