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Accurate computation of Mathieu functions / Malcolm M. Bibby and Andrew F. Peterson

Author
Bibby, Malcolm M.
Published
San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2014.
Physical Description
1 PDF (x, 123 pages) : illustrations
Additional Creators
Peterson, Andrew F., 1960-
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Restrictions on Access
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Contents
1. Introduction --, 2. Mathieu functions -- 2.1 The Mathieu equations -- 2.2 Angular functions -- 2.2.1 Relations satisfied by the expansion functions (A) and (B) -- 2.3 Radial functions -- 2.4 Computational steps -- 2.5 Summary --, 3. Observed accuracy using traditional and tuned methods -- 3.1 Angular functions -- 3.1.1 Subtraction error -- 3.1.2 Back substitution -- 3.2 Radial functions -- 3.3 Example: computing a Hankel function in terms of a summation of Mathieu functions -- 3.4 Summary --, 4. Recommended algorithm for Mathieu function computation -- 4.1 The tuned algorithm -- 4.2 Example: calculation of a uniform plane wave -- 4.3 Adaptive error estimation based on the plane wave -- 4.4 Summary --, 5. Electromagnetic scattering from conducting elliptic cylinders -- 5.1 The TMz case -- 5.2 The TEz case -- 5.3 Examples -- 5.4 The size, N, of the Eigenmatrix for the computations to follow -- 5.5 Current density and scattering cross section for TMz excitation -- 5.6 Current density and scattering cross section for TEz excitation -- 5.7 Summary --, 6. Electromagnetic scattering from an infinite conducting strip -- -- 6.1 The TMz case -- 6.2 The TEz case -- 6.3 Results -- 6.4 Summary --, and A. Converting between two common Mathieu function conventions -- B. Tables of select Eigenvalues and Eigenvectors -- C. Tables of select angular Mathieu functions -- D. Tables of select radial Mathieu functions -- References -- Authors' biographies.
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 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.
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ISBN
9781627050869 (electronic bk.)
9781627050852 (pbk.)
Note
Part of: Synthesis digital library of engineering and computer science.
Series from website.
AVAILABLE ONLINE TO AUTHORIZED PSU USERS.
Bibliography Note
Includes bibliographical references (pages 119-122).
Other Forms
Also available in print.
Technical Details
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
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View MARC record | catkey: 12563852