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• W3116628344 abstract "A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed." @default.
• W3116628344 created "2021-01-05" @default.
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• W3116628344 date "2020-12-30" @default.
• W3116628344 modified "2023-09-26" @default.
• W3116628344 title "A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation" @default.
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• W3116628344 doi "https://doi.org/10.3390/math9010065" @default.
• W3116628344 hasPublicationYear "2020" @default.
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