Abstract
In this paper, we develop a local discontinuous Galerkin (LDG) method for numerically solving the nonlocal one-way water wave equation. Based on the features of fractional derivative, the considered model is first coupled into a classical first derivative and a nonlocal fractional integral. Then LDG algorithm is used in space discretization by properly choosing the numerical fluxes. Numerical examples are provided to show the accuracy and effectiveness.
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