A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Benjamin Akers, Tony Liu and Jonah Reeger
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Benjamin Akers: Department of Mathematics and Statistics, Air Force Institute of Technology, Dayton, OH 45433, USA
Tony Liu: Department of Mathematics and Statistics, Air Force Institute of Technology, Dayton, OH 45433, USA
Jonah Reeger: Independent Researcher, Bellbrook, OH 45305, USA

Mathematics, 2020, vol. 9, issue 1, 1-12

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.

Keywords: radial basis functions; finite difference methods; traveling waves; non-uniform grids (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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