A unified framework for asymptotic analysis and computation of finite Hankel transform
Copyright policy )A unified framework for asymptotic analysis and computation of finite Hankel transform
In this paper we present a unified framework for asymptotic analysis and computation of the finite Hankel transform. This framework enables us to derive asymptotic expansions of the transform, including the cases where the oscillator has zeros and stationary points. As a consequence, two efficient and affordable methods for computing the transform numerically are developed and a detailed analysis of their asymptotic error estimate is carried out. Numerical examples are provided to confirm our analysis.
31 pages
- Huazhong University of Science and Technology China (People's Republic of)
modified Filon-type methods, asymptotic expansion, finite Hankel transform, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Numerical Analysis (math.NA), extended complete Chebyshev system, 65D30, 65D32, 65R10, 41A60, FOS: Mathematics, Special integral transforms (Legendre, Hilbert, etc.), oscillatory integrals, Mathematics - Numerical Analysis, Numerical methods for integral transforms
modified Filon-type methods, asymptotic expansion, finite Hankel transform, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Numerical Analysis (math.NA), extended complete Chebyshev system, 65D30, 65D32, 65R10, 41A60, FOS: Mathematics, Special integral transforms (Legendre, Hilbert, etc.), oscillatory integrals, Mathematics - Numerical Analysis, Numerical methods for integral transforms
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