Efficient Methods for the Chebyshev-Type Prolate Spheroidal Wave Functions and Corresponding Eigenvalues

Yan Tian and Guidong Liu ()
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Yan Tian: College of Science, North China Institute of Science and Technology, Beijing 101601, China
Guidong Liu: School of Mathematics, Nanjing Audit University, Nanjing 211815, China

Mathematics, 2024, vol. 12, issue 6, 1-14

Abstract: This study explores efficient methods for computing eigenvalues and function values associated with Chebyshev-type prolate spheroidal wave functions (CPSWFs). Applying the expansion of the factor e i c x y and the inherent properties of Chebyshev polynomials, we present an exact and stable numerical approximation for the exact eigenvalues of the integral operator to CPSWFs. Additionally, we illustrate the efficiency of employing fast Fourier transform and barycentric interpolation techniques for computing CPSWF values and related quantities, which are essential for various numerical applications based on these functions. The analysis is supported by numerical examples, providing validation for the accuracy and reliability of our proposed approach.

Keywords: spectral method; prolate spheroidal wave functions; Chebyshev polynomial (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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