A new collocation method based on cubic Lidstone Splines is introduced for solving second order BVPs. It derives directly from piecewise Lidstone polynomials of degree 3 by requiring the continuity of the first derivative at the nodal points. For equally spaced nodes it reduces to a classical finite difference method of second order. The estimation of local and global error is given. Finally we solve some numerical problems and we compare the results with those of other methods.

Cubic Lidstone-Spline for numerical solution of BVPs

GUALTIERI, Maria Italia;
2017

Abstract

A new collocation method based on cubic Lidstone Splines is introduced for solving second order BVPs. It derives directly from piecewise Lidstone polynomials of degree 3 by requiring the continuity of the first derivative at the nodal points. For equally spaced nodes it reduces to a classical finite difference method of second order. The estimation of local and global error is given. Finally we solve some numerical problems and we compare the results with those of other methods.
Boundary value problem, Cubic spline, Lidstone polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/132400
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