High-order Higdon non-reflecting boundary conditions for the shallow water equations
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In this report we document the implementation of high order Higdon nonreflecting boundary conditions. We suggest a way to choose the parameters and demonstrate numerically the efficiency of our choice. The model we used is the shallow water equations and as a special case the Klein-Gordon equation. These equations are solved by the finite difference method. We comment on the use of finite elements and demonstrate a new, more efficient method. The case of curved boundary is discussed. We close with a list of topics for research.