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Algorithm 537: Characteristic Values of Mathieu's Differential Equation S22

Algorithm 537: Characteristic Values of Mathieu's Differential Equation S22 ALGORITHM 537 Characteristic Values of Mathieu's Differential Equation [$22] WALTER R. LEEB T e c h n i s c h e Universit&t Wien, Austria Key Words and Phrases. Matbleu's differential equation, wave equation, characteristic values, elgenvalues,separation constants, Mathleu functions, ordinary Mathleu functions, modified Mathmu functions, elliptic cylinder functions, hyperbolic cylinder functions CR Categories 5.14, 5.1 7 Language Fortran DESCRIPTION T h e algorithm calculates the characteristic values b of M a t h i e u ' s differential equation d 2 y / d x 2 + ( b - S cos2x) y -- 0 (1) for solutions y ( x ) of periodicity ~r or 2~r. In this case b is a function of S and belongs to a countably infinite set of values for every S [2]. T h e knowledge of b is a prerequisite for calculating ordinary and modified M a t h i e u functions. T h e p r o g r a m has been tested for real S - p a r a m e t e r s between zero and 1000, and for a n u m b e r of characteristic values of up http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

Algorithm 537: Characteristic Values of Mathieu's Differential Equation S22

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1979 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/355815.355824
Publisher site
See Article on Publisher Site

Abstract

ALGORITHM 537 Characteristic Values of Mathieu's Differential Equation [$22] WALTER R. LEEB T e c h n i s c h e Universit&t Wien, Austria Key Words and Phrases. Matbleu's differential equation, wave equation, characteristic values, elgenvalues,separation constants, Mathleu functions, ordinary Mathleu functions, modified Mathmu functions, elliptic cylinder functions, hyperbolic cylinder functions CR Categories 5.14, 5.1 7 Language Fortran DESCRIPTION T h e algorithm calculates the characteristic values b of M a t h i e u ' s differential equation d 2 y / d x 2 + ( b - S cos2x) y -- 0 (1) for solutions y ( x ) of periodicity ~r or 2~r. In this case b is a function of S and belongs to a countably infinite set of values for every S [2]. T h e knowledge of b is a prerequisite for calculating ordinary and modified M a t h i e u functions. T h e p r o g r a m has been tested for real S - p a r a m e t e r s between zero and 1000, and for a n u m b e r of characteristic values of up

Journal

ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery

Published: Mar 1, 1979

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