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Algorithm 914: Parabolic cylinder function W(a, x) and its derivative

Authors:

Amparo Gil,

Javier Segura,

Nico M. TemmeAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 38, Issue 1

Article No.: 6, Pages 1 - 5

https://doi.org/10.1145/2049662.2049668

Published: 07 December 2011 Publication History

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Abstract

A Fortran 90 program for the computation of the real parabolic cylinder functions W(a, ± x), x ≥ 0 and their derivatives is presented. The code also computes scaled functions for a > 50. The functions W(a, ± x) are a numerically satisfactory pair of solutions of the parabolic cylinder equation y′ + (x²/4 − a)y = 0, x ≥ 0. Using Wronskian tests, we claim a relative accuracy better than 5 10⁻¹³ in the computable range of unscaled functions, while for scaled functions the aimed relative accuracy is better than 5 10⁻¹⁴. This code, together with the algorithm and related software described in Gil et al. [2006a, 2006b], completes the set of software for Parabolic Cylinder Functions (PCFs) for real arguments.

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References

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Cited By

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Dunster TGil ASegura J(2024)Computation of parabolic cylinder functions having complex argumentApplied Numerical Mathematics10.1016/j.apnum.2023.11.017197:C(230-242)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.apnum.2023.11.017
Moran-Lopez ACorcoles JRuiz-Cruz JMontejo-Garai JRebollar J(2018)Robust Calculation of the Modes in Parabolic Cylinder Metallic Waveguides by Means of a Root-Finding Method for Bivariate FunctionsIEEE Transactions on Microwave Theory and Techniques10.1109/TMTT.2017.277796966:2(623-632)Online publication date: Feb-2018
https://doi.org/10.1109/TMTT.2017.2777969
Moran-Lopez ACorcoles JRuiz-Cruz JMontejo-Garai JRebollar J(2017)Direct computation of parabolic waveguide modes via a bivariate root-finding algorithm2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO)10.1109/NEMO.2017.7964217(152-154)Online publication date: May-2017
https://doi.org/10.1109/NEMO.2017.7964217
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Index Terms

Algorithm 914: Parabolic cylinder function W(a, x) and its derivative
1. Mathematics of computing
  1. Mathematical software

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 38, Issue 1

November 2011

144 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2049662

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 07 December 2011

Accepted: 01 April 2011

Received: 01 September 2010

Published in TOMS Volume 38, Issue 1

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Cited By

View all

Dunster TGil ASegura J(2024)Computation of parabolic cylinder functions having complex argumentApplied Numerical Mathematics10.1016/j.apnum.2023.11.017197:C(230-242)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1016/j.apnum.2023.11.017
Moran-Lopez ACorcoles JRuiz-Cruz JMontejo-Garai JRebollar J(2018)Robust Calculation of the Modes in Parabolic Cylinder Metallic Waveguides by Means of a Root-Finding Method for Bivariate FunctionsIEEE Transactions on Microwave Theory and Techniques10.1109/TMTT.2017.277796966:2(623-632)Online publication date: Feb-2018
https://doi.org/10.1109/TMTT.2017.2777969
Moran-Lopez ACorcoles JRuiz-Cruz JMontejo-Garai JRebollar J(2017)Direct computation of parabolic waveguide modes via a bivariate root-finding algorithm2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO)10.1109/NEMO.2017.7964217(152-154)Online publication date: May-2017
https://doi.org/10.1109/NEMO.2017.7964217
Pearson JOlver SPorter M(2017)Numerical methods for the computation of the confluent and Gauss hypergeometric functionsNumerical Algorithms10.1007/s11075-016-0173-074:3(821-866)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1007/s11075-016-0173-0
Gil ASegura JTemme N(2014)Recent software developments for special functions in the Santander-Amsterdam projectScience of Computer Programming10.1016/j.scico.2013.11.00490:PA(42-54)Online publication date: 15-Sep-2014
https://dl.acm.org/doi/10.1016/j.scico.2013.11.004

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Algorithm 850: Real parabolic cylinder functions U(a, x), V(a, x)

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Nield--Kuznetsov Functions and Laplace Transforms of Parabolic Cylinder Functions