Accurate computation of Mathieu functions

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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Bibliographic Details
Main Authors: Bibby, Malcolm M. (Author), Peterson, Andrew F., 1960- (Author)
Format: Electronic eBook
Language:English
Published: Cham, Switzerland : Springer, [2014]
Series:Synthesis lectures on computational electromagnetics ; #32.
Subjects:
Mathieu functions.
Online Access:Connect to this title online
Table of 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.
  • 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.

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