Lidstone polynomials and boundary value problems
type: Item
instance of: scholarly article
title: Lidstone polynomials and boundary value problems
zbMATH Open document ID: 0682.65049
DOI: 10.1016/0898-1221(89)90023-0
author: Ravi P. Agarwal
author: Patricia J. Y. Wong
publication date: 1989-01-01T00:00:00Z
review text: The interpolation polynomial of degree 2m-1 of a given function \(y=y(x)\) given by \textit{G. J. Lidstone} [Proc. Edinb. Math. Soc. 2(2), 16-19 (1930; JFM 56.1053.03)] matches \(y,y^{(2)},y^{(4)},...,y^{(m-1)}\) at \(x=0\) and \(x=1\). The authors provide a number of results on Lidstone interpolation and on the related two-point boundary value problem \(y^{(2m)}=F(x,y,y^{(1)},...,y^{(2m-1)})\) with \(y,y^{(2)},y^{(4)},...,y^{(m-1)}\) given at \(x=0\) and \(x=1\). (Note that when \(F\equiv 0\) this problem is solved by a Lidstone polynomial.)
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 4117774
zbMATH Keywords: Bernoulli polynomials
zbMATH Keywords: error estimates
zbMATH Keywords: best possible/sharp inequalities
zbMATH Keywords: Euler polynomials
zbMATH Keywords: Euler numbers
zbMATH Keywords: Picard iterative sequence
zbMATH Keywords: Lidstone interpolation
zbMATH Keywords: boundary value problem
reviewed by: Jesús María Sanz-Serna
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90023-0
OpenAlex ID: W1971651923
cites work: A note on functions of exponential type
cites work: Representation of functions by Lidstone series
cites work: On certain two-point expansions of integral functions of exponential type
cites work: On Lidstone's Series and Two-Point Expansions of Analytic Functions
cites work: Functions Whose Even Derivatives Have a Prescribed Sign
cites work: Completely Convex Functions and Lidstone Series
cites work: Q3848301
cites work: Q3732891
cites work: Numerical methods for unilateral problems
cites work: Solving Boundary Value Problems in Plate Deflection Theory
cites work: Boundary value problems occurring in plate deflection theory
cites work: Finite difference methods for two-point boundary value problems involving high order differential equations
cites work: The special functions and their approximations. Vol. I, II
cites work: Q5786094
cites work: Q4753589
cites work: Best error bounds for derivatives in two point Birkhoff interpolation problems
cites work: Q3807603
cites work: Monotone convergence of iterative methods for (n,p) and (p,n) boundary value problems
cites work: Monotone convergence of iterative methods for right focal point boundary value problems
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4117774