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

Abstract

We 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.

Bivariate general Appell interpolation problem

“…On the other hand, interpolation is fundamental in numerical approximation of functions, numerical quadrature and cubature, boundary value methods, etc. [12,16,17,28]. In an interpolation problem the choice of basic functions, that is the system {φ n } n∈IN , is very important.A.…”