An analysis of higher order boundary conditions for the wave equation

Thanks to the use of the Cagniard-De Hoop method, we derive an analytic solution in the time domain for the half-space problem associated with the wave equation with Engquist-Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to +∞, as well as error estimates. The theory is illustrated by numerical results.