Result: Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms
Title:
Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms
Authors:
Source:
Journal of Computational Physics. 199:688-716
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
Lamé, Mathieu, and spheroidal wave functions, pseudospectral method, numerical weather prediction, Chebyshev polynomial, 01 natural sciences, Computation of special functions and constants, construction of tables, quasi-uniform spectral scheme, Legendre polynomials, Spectral, collocation and related methods for boundary value problems involving PDEs, Numerical approximation and evaluation of special functions, spectral elements, 0101 mathematics, Spherical harmonics, prolate spheroidal wavefunctions
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0021-9991
DOI:
10.1016/j.jcp.2004.03.010
Access URL:
https://zbmath.org/2107342
https://doi.org/10.1016/j.jcp.2004.03.010
https://www.sciencedirect.com/science/article/pii/S0021999104001123
https://dl.acm.org/doi/10.1016/j.jcp.2004.03.010
http://www.sciencedirect.com/science/article/pii/S0021999104001123
https://ui.adsabs.harvard.edu/abs/2004JCoPh.199..688B/abstract
https://doi.org/10.1016/j.jcp.2004.03.010
https://www.sciencedirect.com/science/article/pii/S0021999104001123
https://dl.acm.org/doi/10.1016/j.jcp.2004.03.010
http://www.sciencedirect.com/science/article/pii/S0021999104001123
https://ui.adsabs.harvard.edu/abs/2004JCoPh.199..688B/abstract
Rights:
Elsevier TDM
Accession Number:
edsair.doi.dedup.....35a7e193841124fd4047cc23f749d68f
Database:
OpenAIRE
Further Information
Prolate spheroidal functions of order zero are generalizations of Legendre functions which oscillate more uniformly than either Legendre or Chebyshev polynomials. This suggests that prolate functions yield more uniform spatial resolution and allow a longer stable timestep than Legendre polynomials. It is shown that these advantages are real and that it is trivial to modify existing pseudospectral or spectral element codes to use the prolate basis. The prolate basis is not likely to radically expand the range of problems but it is expected that there are improvements for applications, such as numerical weather prediction.