Convergence of regularized spline approximants to solutions of initial and boundary value problems for ODE
type: Item
instance of: scholarly article
title: Convergence of regularized spline approximants to solutions of initial and boundary value problems for ODE
zbMATH Open document ID: 0830.65069
DOI: 10.1016/0377-0427(93)E0267-P
author: Valery P. Voevudsky
published in: Journal of Computational and Applied Mathematics
publication date: 1996-02-04T00:00:00Z
review text: For linear initial and boundary value problems for ordinary differential equations (ODEs) spline collocation is a well-known numerical method. This paper deals with the case when the right-hand side of the equation, given on a discrete mesh, includes errors. Following Tikhonov's regularization technique the author investigates the spline approximant as a solution for a minimizing problem. Existence and uniqueness of the solution together with convergence rates are proved. The results are presented for linear initial value problems. A modification for linear boundary value problems with zero boundary condition is possible.
reviewed by: Z.Schneider
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 777853
zbMATH Keywords: spline collocation
zbMATH Keywords: Tikhonov's regularization
zbMATH Keywords: convergence
zbMATH Keywords: initial value problems
zbMATH Keywords: boundary value problems
MaRDI profile type: Publication
cites work: Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
cites work: How small can one make the derivatives of an interpolating function?
cites work: Q3797561
cites work: Error bounds for derivative estimates based on spline smoothing of exact or noisy data
cites work: Q3806712
cites work: Q4042609
full work available at URL: 0377-0427(93)e0267-p
OpenAlex ID: W2092669564
Recommended article: Q4283937
Recommended article: Q4010822
Recommended article: Q5458718
Recommended article: On the Asymptotic Convergence of Spline Collocation Methods for Partial Differential Equations
Recommended article: Q4231586
Recommended article: Some Uniformly Convergent Spline Difference Schemes for Singularly Parturbed Boundary Value Problems
Recommended article: Q3159086
Recommended article: Convergence of cubic-spline approach to the solution of a system of boundary-value problems
Recommended article: Convergence analysis of spline solution of certain two-point boundary value problems
Recommended article: Q3833544
description: scientific article; zbMATH DE number 777853