The computation of eigenvalues and solutions of Mathieu's differential equation for noninteger order

DOI10.1145/155743.155796zbMath0892.65057OpenAlexW1964028571WikidataQ113310522 ScholiaQ113310522MaRDI QIDQ4371546

Randall B. Shirts

Publication date: 26 January 1998

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: http://www.acm.org/pubs/contents/journals/toms/1993-19/

zbMATH Keywords

algorithmsNewton's methodeigenvaluesasymptotic expansionsTaylor serieseigenfunction expansioncontinued fraction expansionFourier series expansionMathieu's differential equation

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (4)

Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid ⋮ The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials ⋮ Power series expansions for Mathieu functions with small arguments ⋮ New method to obtain small parameter power series expansions of Mathieu radial and angular functions

Uses Software

• MTIEU1

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