Positive solutions of complementary Lidstone boundary value problems

We consider the following complementary Lidstone boundary value problem (−1)my (2m+1)(t) = F(t, y(t), y′ (t)), t ∈ [0, 1] y(0) = 0, y(2k−1)(0) = y (2k−1)(1) = 0, 1 ≤ k ≤ m. The nonlinear term F depends on y ′ and this derivative dependence is seldom investigated in the literature. Using a variety of fixed point theorems, we establish the existence of one or more positive solutions for the boundary value problem. Examples are also included to illustrate the results obtained.Published versio

Odd and Even Lidstone-type polynomial sequences. Part 1: basic topics

Abstract Two new general classes of polynomial sequences called respectively odd and even Lidstone-type polynomials are considered. These classes include classic Lidstone polynomials of first and second kind. Some characterizations of the two classes are given, including matrix form, conjugate sequences, generating function, recurrence relations, and determinant forms. Some examples are presented and some applications are sketched

Lidstone–Euler interpolation and related high even order boundary value problem

AbstractWe consider the Lidstone–Euler interpolation problem and the associated Lidstone–Euler boundary value problem, in both theoretical and computational aspects. After a theorem of existence and uniqueness of the solution to the Lidstone–Euler boundary value problem, we present a numerical method for solving it. This method uses the extrapolated Bernstein polynomials and produces an approximating convergent polynomial sequence. Particularly, we consider the fourth-order case, arising in various physical models. Finally, we present some numerical examples and we compare the proposed method with a modified decomposition method for a tenth-order problem. The numerical results confirm the theoretical and computational ones

A Chronology of Interpolation: From Ancient Astronomy to Modern Signal and Image Processing

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation

Aeronautical engineering: A continuing bibliography with indexes (supplement 240)

This bibliography lists 629 reports, articles, and other documents introduced into the NASA scientific and technical information system in May, 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics