Algorithm 721: MTIEU1 and MTIEU2

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Algorithm 721: MTIEU1 and MTIEU2: two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 19 , Issue 3 (September 1993) table of contents

Pages: 391 - 406

Year of Publication: 1993

ISSN:0098-3500

Author

Randall B. Shirts

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 48, Citation Count: 4

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appendices and supplements abstract references cited by index terms

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eigenvalues of Mathieu differential equation for noninteger and integer order
Gams: c17

ABSTRACT

Two FORTRAN routines are described which calculate eigenvalues and eigenfunctions of Mathieu's differential equation for noninteger as well as integer order, MTIEU1 uses standard matrix techniques with dimension parameterized to give accuracy in the eigenvalue of one part in 1012. MTIEU2 used continued fraction techniques and is optimized to give accuracy in the eigenvalue of one part in 1014. The limitations of the algorithms are also discussed and illustrated.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BL&NCH, G. Numerical aspects of Mathieu eigenvalues. Rend. Ctrc. Mat. Palermo., Ser. 2, 15, i (Jan. 1966) 51 97.
	2	BLANCH, G. Mathieu functions. In Handbook of Mathematical Functions, M. I. Abramowitz, and I. A Stegun, Eds. Dover, New York, 1970, Ch. 20, 722-750.
	3	Donald S. Clemm, Algorithm 352: characteristic values and associated solutions of Mathieu's differential equation [S22], Communications of the ACM, v.12 n.7, p.399-407, July 1969 [doi>10.1145/363156.363176]
	4	DINGLE, R. B., AND MULLER, H. J.W. Asymptotic expansions of Mathieu functions and their characteristic numbers. J. Angew, Math. 211, i (Jan. 1962), 11 32.
	5	Walter R. Leeb, Algorithm 537: Characteristic Values of Mathieu's Differential Equation [S22], ACM Transactions on Mathematical Software (TOMS), v.5 n.1, p.112-117, March 1979 [doi>10.1145/355815.355824]
	6	THE GROUP "NUMERICAL ANALYSIS" at Delf Umversity of Technology. On the computation of Mathieu functions. J. Eng. Math. 7, I (Jan. 1973), 39-61.
	7	TOYAMA, N., AND SHOGEN, K. Computation of the value of the even and odd Mathieu functions of order N for a given parameter S and an argument X. IEEE Trans Ant. Prop AP32, 5 (May 1984), 537-539.

CITED BY 4

	Fayez A. Alhargan, Algorithms for the computation of all Mathieu functions of integer orders, ACM Transactions on Mathematical Software (TOMS), v.26 n.3, p.390-407, Sept. 2000
	Fayez A. Alhargan, Algorithm 804: subroutines for the computation of Mathieu functions of integer orders, ACM Transactions on Mathematical Software (TOMS), v.26 n.3, p.408-414, Sept. 2000
	Fayez A. Alhargan, Algorithm 855: Subroutines for the computation of Mathieu characteristic numbers and their general orders, ACM Transactions on Mathematical Software (TOMS), v.32 n.3, p.472-484, September 2006
	Danilo Erricolo, Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch's algorithm, ACM Transactions on Mathematical Software (TOMS), v.32 n.4, p.622-634, December 2006