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

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 so...

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Bibliographic Details
Published in:Calcolo 2021-06, Vol.58 (2), Article 25
Main Authors: Costabile, Francesco Aldo, Gualtieri, Maria Italia, Napoli, Anna
Format: Article
Language:English
Subjects:
Boundary value problems
Existence theorems
Interpolation
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical methods
Polynomials
Theory of Computation
Uniqueness theorems
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Summary: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.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-021-00411-y