Highly Efficient and Accurate Spectral Approximation of the Angular Mathieu Equation for any Parameter Values $q$
Year: 2018
Author: Haydar Alıcı, Jie Shen
Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 131–149
Abstract
The eigenpairs of the angular Mathieu equation under the periodicity condition are accurately approximated by the Jacobi polynomials in a spectral-Galerkin scheme for small and moderate values of the parameter $q.$ On the other hand, the periodic Mathieu functions are related with the spheroidal functions of order $±1/2.$ It is well-known that for very large values of the bandwidth parameter, spheroidal functions can be accurately approximated by the Hermite or Laguerre functions scaled by the square root of the bandwidth parameter. This led us to employ the Laguerre polynomials in a pseudospectral manner to approximate the periodic Mathieu functions and the corresponding characteristic values for very large values of $q.$
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v51n2.18.02
Journal of Mathematical Study, Vol. 51 (2018), Iss. 2 : pp. 131–149
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Mathieu function spectral methods Jacobi polynomials Laguerre polynomials.