Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms

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

ON BERNOULLI BOUNDARY VALUE PROBLEM

We give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard’s iteration. Moreover Newton’s iteration method is considered for the numerical computation of the solution.We give a constructive proof of the existence and uniqueness of thesolution, under certain conditions, by Picard’s iteration. MoreoverNewton’s iteration method is considered for the numerical computation of the solution

Interpolation problems and applications

Dottorato di Ricerca in Matematica ed Informatca CICLO XXI, a.a.2008-2009Università della Calabri