@article{10902/3207,
year = {2010},
month = {4},
url = {http://hdl.handle.net/10902/3207},
abstract = {A fourth order fixed point method to compute the zeros of solutions of second order
homogeneous linear ODEs is obtained from the approximate integration of the Riccati equation
associated with the ODE. The method requires the evaluation of the logarithmic derivative of the
function and also uses the coefficients of the ODE. An algorithm to compute with certainty all the
zeros in an interval is given which provides a fast, reliable, and accurate method of computation.
The method is illustrated by the computation of the zeros of Gauss hypergeometric functions (including
Jacobi polynomials) and confluent hypergeometric functions (Laguerre polynomials, Hermite
polynomials, and Bessel functions included) among others. The examples show that typically 4 or 5
iterations per root are enough to provide more than 100 digits of accuracy, without requiring a priori
estimations of the roots.},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Numerical Analysis, Vol. 48, No. 2, pp. 452–469},
title = {Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method},
author = {Segura Sala, José Javier},
}