Description

Book Synopsis
This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

Table of Contents
Introduction.- Mathieu Functions.- Observed Accuracy Using Traditional and Tuned Methods.- Recommended Algorithm for Mathieu Function Computation.- Electromagnetic Scattering from Conducting Elliptic Cylinders.- Electromagnetic Scattering from an Infinite Conducting Strip.- References.- Authors' Biographies.

Accurate Computation of Mathieu Functions

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    A Paperback by Andrew Peterson, Malcolm Bibby

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      Book details

      Publisher Springer International Publishing AG
      Published 15 October 2013
      ISBN-13 9783031005893
      978-3031005893
      ISBN-10 3031005899

      Description

      Book Synopsis
      This lecture presents a modern approach for the computation of Mathieu functions. These functions find application in boundary value analysis such as electromagnetic scattering from elliptic cylinders and flat strips, as well as the analogous acoustic and optical problems, and many other applications in science and engineering. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned" approach enabling improved accuracy and convergence. The performance of this approach is investigated for a wide range of parameters and machine precision. Examples from electromagnetic scattering are provided for illustration and to show the convergence of the typical series that employ Mathieu functions for boundary value analysis.

      Table of Contents
      Introduction.- Mathieu Functions.- Observed Accuracy Using Traditional and Tuned Methods.- Recommended Algorithm for Mathieu Function Computation.- Electromagnetic Scattering from Conducting Elliptic Cylinders.- Electromagnetic Scattering from an Infinite Conducting Strip.- References.- Authors' Biographies.

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