Rational Approximation for Two-Point Boundary value problems

Details Rational Approximation for Two-Point Boundary value problems Rational Approximation for Two-Point Boundary value problems

2007-05-25

arxiv.org/abs/0705.3862v1

Physics

Mathematical Physics

13 pages, 1 figure

Scientific paper

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.

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