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Ordinary differential equation algorithms for a frequency-domain water wave Green’s function. (English) Zbl 1379.76009

Summary: Our study investigated an algorithm for a second-order ordinary differential equation for the frequency-domain Green’s function of free-surface waves in water of infinite depth. A power-series method is introduced if the wave frequency \(\omega <1\); otherwise, if \(\omega \geq 1\), then the trigonometrically fitted block Numerov-type method (TBNM) is employed. The calculation precision of the power-series method and the TBNM reached \(10^{-7}\) and \(10^{-6}\), respectively. The two methods have a high calculation efficiency compared with calculating the Green’s function using the series expansion representation approach. The calculation speed for these two methods is 15 times faster using the same computing codes.

MSC:

76B07 Free-surface potential flows for incompressible inviscid fluids
65L05 Numerical methods for initial value problems involving ordinary differential equations
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
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