Algorithm 861

Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. A translation to Fortran 90 of Gertrude Blanch’s algorithm for computing the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use, and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented.

This software is also peer reviewed by journal TOMS.

Keywords for this software

computational fluid dynamics
biological fluid dynamics
Mathieu function
transformation of series
pulsatile flow
continued fractions
plastic flow
finite volume methods
linear recurrence relations
asymptotic analysis
Chebyshev expansions
quadrature methods
laminar flow
computation
special function
numerical evaluation of special functions
validation
numerical examples
Navier-Stokes equations

References in zbMATH (referenced in 5 articles )

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Sorted by year (citations)

Erricolo, Danilo; Carluccio, Giuseppe: Algorithm 934: Fortran 90 subroutines to compute Mathieu functions for complex values of the parameter (2013)
Gil, Amparo; Segura, Javier; Temme, Nico M.: Basic methods for computing special functions (2011)
Larsen, T. M.; Erricolo, D.; Uslenghi, P. L. E.: New method to obtain small parameter power series expansions of Mathieu radial and angular functions (2009)
Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan: Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid (2008)
Erricolo, Danilo: Algorithm 861: Fortran 90 subroutines for computing the expansion coefficients of Mathieu functions using Blanch’s algorithm. (2006)