Rational Approximation to the Solutions of Two-Point Boundary Value Problems

P. Amore, F. M. Fernández

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 fixed point equation in the local potential approximation, and a Riccati equation. We consider two models where the approach does not apply in order to show the limitations of our Padé-Hankel approach.

Keywords


nonlinear differential equations; Ginzburg-Landau; Wilson’s renormalization; Wegner-Houghton; Riccati equation; Padé-Hankel method

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague