Rational Approximation for Two-Point Boundary value problems
Mathematical Physics
2007-05-29 v1 math.MP
Abstract
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown parameter of the problem. We treat several problems of physical interest: the field equation determining the vortex profile in a Ginzburg--Landau effective theory, the fixed--point equation for Wilson's exact renormalization group, a suitably modified Wegner--Houghton's fixed point equation in the local potential approximation, a Riccati equation, and the Thomas--Fermi equation. We consider two models where the approach does not apply in order to show the limitations of our Pad\'{e}--Hankel approach.
Keywords
Cite
@article{arxiv.0705.3862,
title = {Rational Approximation for Two-Point Boundary value problems},
author = {Paolo Amore and Francisco M. Fernandez},
journal= {arXiv preprint arXiv:0705.3862},
year = {2007}
}