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Accurate calculations of Mathieu functions

Author: Malcolm M Bibby; Andrew F Peterson
Publisher: [San Rafael, California] : Morgan & Claypool, [2014] ©2014
Series: Synthesis lectures on computational electromagnetics, #32.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bibby, Malcolm M.
Accurate Computation of Mathieu Functions.
San Rafael : Morgan & Claypool Publishers, ©2013
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Malcolm M Bibby; Andrew F Peterson
ISBN: 9781627050869 1627050868 162705085X 9781627050852
OCLC Number: 865854106
Description: 1 online resource (135 pages) : illustrations.
Contents: Introduction; Mathieu Functions; The Mathieu Equations; Angular Functions; Relations Satisfied by the Expansion Functions { A } and { B }; Radial Functions; Computational Steps; Summary; Observed Accuracy Using Traditional and Tuned Methods; Angular Functions; Subtraction Error; Back Substitution; Radial Functions; Example: Computing a Hankel Function in Terms of a Summation of Mathieu Functions; Summary; Recommended Algorithm for Mathieu Function Computation; The Tuned Algorithm; Example: Calculation of a Uniform Plane Wave; Adaptive Error Estimation Based on the Plane Wave; Summary. Electromagnetic Scattering from Conducting Elliptic CylindersThe TM_z Case; The TE_z Case; Examples; The Size, N, of the Eigenmatrix for the Computations to Follow; Current Density and Scattering Cross Section for TM_z Excitation; Current Density and Scattering Cross Section for TE_z Excitation; Summary; Electromagnetic Scattering from an Infinite Conducting Strip; The TM_z Case; The TE_z Case; Results; Summary; Converting Between Two Common Mathieu Function Conventions; Tables of Select Eigenvalues and Eigenvectors; Tables of Select Angular Mathieu Functions. Tables of Select Radial Mathieu FunctionsReferences; Authors' Biographies.
Series Title: Synthesis lectures on computational electromagnetics, #32.
Responsibility: Malcolm M. Bibby, Andrew F. Peterson.

Abstract:

Presents a modern approach for the computation of Mathieu functions. The authors review the traditional approach used for these functions, show its limitations, and provide an alternative "tuned"  Read more...

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