2014/08/01 by Ross Adelman, Adelman, Ross, Nail A. Gumerov +3
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Geodetic Measurements and Engineering Structures #Geophysics and Gravity Measurements #Mathematical Analysis and Transform Methods #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1408.0074
openalex publication_date 2014/08/01 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The spheroidal wave functions, which are the solutions to the Helmholtz\nequation in spheroidal coordinates, are notoriously difficult to compute.\nBecause of this, practically no programming language comes equipped with the\nmeans to compute them. This makes problems that require their use hard to\ntackle. We have developed computational software for calculating these special\nfunctions. Our software is called spheroidal and includes several novel\nfeatures, such as: using arbitrary precision arithmetic; adaptively choosing\nthe number of expansion coefficients to compute and use; and using the\nWronskian to choose from several different methods for computing the spheroidal\nradial functions to improve their accuracy. There are two types of spheroidal\nwave functions: the prolate kind when prolate spheroidal coordinates are used;\nand the oblate kind when oblate spheroidal coordinate are used. In this paper,\nwe describe both, methods for computing them, and our software. We have made\nour software freely available on our webpage.\n