Lidstone polynomials and boundary value problems. (English) Zbl 0682.65049

The interpolation polynomial of degree 2m-1 of a given function \(y=y(x)\) given by 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.)
Reviewer: J.M.Sanz-Serna


65L10 Numerical solution of boundary value problems involving ordinary differential equations
41A05 Interpolation in approximation theory
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
34B05 Linear boundary value problems for ordinary differential equations


JFM 56.1053.03
Full Text: DOI


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