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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