Constructive polynomial approximation with \textit{a priori} error bounds for nonlinear initial value differential problems
type: Item
instance of: scholarly article
title: Constructive polynomial approximation with \textit{a priori} error bounds for nonlinear initial value differential problems
zbMATH Open document ID: 0947.34007
DOI: 10.1016/S0898-1221(99)00233-3
author: A. E. Posso
author: H. Casteljón
author: L. Jódar
publication date: 2000-04-11T00:00:00Z
review text: The authors obtain an approximate solution to the initial value problem \[ y'=f(x,y), \quad y(0)=y_0, \] where \(f\) is continuous and is Lipschitzian with respect to each argument when the other is fixed. First, \(f(x,y)\) is approximated by a sequence \(\{B_n(f; x,y)\}\) of Bernstein polynomials in two variables of an appropriate degree according to a prescribed accuracy. Then an exact series solution to \(y'=B_n (f;x,y)\), \(y(0)=y_0\), is constructed by the Frobenius method. Finally, the infinite series solution is truncated in order to obtain an explicit polynomial whose error with respect to the exact solution of the original problem is less than the prescribed accuracy.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 1429527
zbMATH Keywords: approximate solution
zbMATH Keywords: initial value problem
zbMATH Keywords: Frobenius method
zbMATH Keywords: Bernstein polynomials
MaRDI profile type: Publication
cites work: Q5719651
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full work available at URL: s0898-1221(99)00233-3
OpenAlex ID: W2032388268
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1429527