Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch's algorithm

A translation to Fortran 90 of Gertrude Blanch's algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented.

[1]  D. Erricolo,et al.  Exact radiation and scattering for an elliptic metal cylinder at the interface between isorefractive half-spaces , 2004, IEEE Transactions on Antennas and Propagation.

[2]  D. Erricolo,et al.  Currents on conducting surfaces of a semielliptical-channel-backed slotted screen in an isorefractive environment , 2005, IEEE Transactions on Antennas and Propagation.

[3]  Gertrude Blanch,et al.  Numerical aspects of Mathieu eigenvalues , 1966 .

[4]  N. Mclachlan.  Theory and Application of Mathieu Functions , 1965 .

[5]  J. Swinburne.  Electromagnetic Theory , 1894, Nature.

[6]  D. B. Hodge.  The calculation of the eigenvalues and eigenfunctions of Mathieu's equation , 1972 .

[7]  Danilo Erricolo,et al.  Scattering by a Blade on a Metallic Plane , 2006 .

[8]  Randall B. Shirts.  Algorithm 721: MTIEU1 and MTIEU2: two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order , 1993, TOMS.

[9]  Fayez A. Alhargan,et al.  Algorithms for the computation of all Mathieu functions of integer orders , 2000, TOMS.

[10]  E. Mathieu.  Mémoire sur le mouvement vibratoire d'une membrane de forme elliptique. , 1868 .

[11]  Louis Baker,et al.  C mathematical function handbook , 1991 .

[12]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[13]  Thomas B. A. Senior,et al.  Electromagnetic and acoustic scattering by simple shapes (Revised edition) , 1987 .

[14]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[15]  D. Erricolo,et al.  Penetration, radiation, and scattering for a cavity-backed gap in a corner , 2005, IEEE Transactions on Antennas and Propagation.

[16]  A V Hershey,et al.  Computation of Special Functions , 1978 .

[17]  T. Senior,et al.  Electromagnetic and Acoustic Scattering by Simple Shapes , 1969 .

[18]  D. Erricolo,et al.  Acceleration of the convergence of series containing Mathieu functions using Shanks transformation , 2003, IEEE Antennas and Wireless Propagation Letters.

[19]  Danilo Erricolo,et al.  NUMERICAL ANALYSIS OF PENETRATION, RADIATION, AND SCATTERING FOR A 2D SLOTTED SEMIELLIPTICAL CHANNEL FILLED WITH ISOREFRACTIVE MATERIAL , 2005 .

[20]  Arthur H. J. Sale.  Remark on algorithms 352: characteristic values and associated solutions of Mathieu's differential equation , 1970, CACM.

[21]  J. Meixner,et al.  Mathieusche Funktionen und Sphäroidfunktionen , 1954 .

[22]  E. L. Ince.  XXII.—Tables of the Elliptic-cylinder Functions , 1933 .

[23]  Randall B. Shirts,et al.  The computation of eigenvalues and solutions of Mathieu's differential equation for noninteger order , 1993, TOMS.

[24]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .