Accurate computation of Mathieu functions /
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 application...
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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
[2014]
|
| Series: | Synthesis lectures on computational electromagnetics ;
#32. |
| Subjects: | |
| Online Access: | Connect to this title online |
MARC
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| 100 | 1 | |a Bibby, Malcolm M., |e author. |0 http://id.loc.gov/authorities/names/no2010132681 | |
| 245 | 1 | 0 | |a Accurate computation of Mathieu functions / |c Malcolm M. Bibby and Andrew F. Peterson. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2014] | |
| 300 | |a 1 online resource (x, 123 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Synthesis lectures on computational electromagnetics, |x 1932-1716 ; |v #32 | |
| 504 | |a Includes bibliographical references (pages 119-122). | ||
| 505 | 0 | |a 1. Introduction. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 6. Electromagnetic scattering from an infinite conducting strip -- -- 6.1 The TMz case -- 6.2 The TEz case -- 6.3 Results -- 6.4 Summary. | |
| 505 | 8 | |a 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. | |
| 510 | 0 | |a Compendex | |
| 510 | 0 | |a INSPEC | |
| 510 | 0 | |a Google scholar | |
| 510 | 0 | |a Google book search | |
| 520 | 3 | |a 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. | |
| 588 | 0 | |a Online resource; title from PDF title page (Morgan & Claypool, viewed on October 16, 2013). | |
| 650 | 0 | |a Mathieu functions. |0 http://id.loc.gov/authorities/subjects/sh85082191 | |
| 650 | 7 | |a Mathieu functions. |2 fast |0 (OCoLC)fst01012375 |0 http://id.worldcat.org/fast/1012375 | |
| 700 | 1 | |a Peterson, Andrew F., |d 1960- |e author. |0 http://id.loc.gov/authorities/names/n97083614 | |
| 740 | 0 | |a Springer Nature Synthesis Collection of Technology Collection 5. | |
| 776 | 0 | 8 | |i Print version: |z 9781627050852 |
| 830 | 0 | |a Synthesis lectures on computational electromagnetics ; |v #32. |0 http://id.loc.gov/authorities/names/no2008017497 | |
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