@article{10902/36372,
year = {2025},
month = {6},
url = {https://hdl.handle.net/10902/36372},
abstract = {A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function U (a, z) in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly efficient method based on a fourth-order fixed point method with the parabolic cylinder functions computed by Taylor series and carefully selected steps, to compute the rest of the zeros. For |a| small, the asymptotic approximations are complemented with a few fixed point iterations requiring the evaluation of U (a, z) and U' (a,z) in the region where the complex zeros are located. Liouville Green expansions are derived to enhance the performance of a computational scheme to evaluate U (a, z) and U' (a,z) in that region. Several tests show the accuracy and efficiency of the numerical algorithm.},
organization = {Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Financial support was received from Ministerio de Economía y Competitividad, Project PID2021-127252NB-I00 (MCIN/AEI/10.13039/501100011033/ FEDER, UE.},
publisher = {Springer Nature},
publisher = {BIT numerical mathematics, 2025, 65(2), 20},
title = {A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane},
author = {Dunster, T.M. and Gil Gómez, Amparo and Ruiz Antolín, Diego and Segura Sala, José Javier},
}