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.

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

Costabile F. A.;Gualtieri M. I.;Napoli A.
2021-01-01

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.
2021
Bernstein polynomials
Boundary value problem
Euler polynomials
Extrapolation
Interpolation
Lidstone polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/327618
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