Absorbing Boundary Conditions of the Second Order for the Pseudospectral Chebyshev Methods for Wave Propagation

In this paper we describe the implementation of one-way wave equations of the second order in conjuction with pseudospectral methods for wave propagation in two space dimensions. These equations are first reformulated as hyperbolic systems of the first order and the absorbing boundaries are implemented by an appropriate modification of the matrix of this system. The resulting matrix corresponding to one-way wave equation based on Padé approximation has all eigenvalues in the complex negative half plane which allows stable integration of the underlying system by any ODE solver in the sense of "eigenvalue stability." The obtained numerical scheme is much more accurate than the schemes obtained before which utilized absorbing boundary conditions of the first order, and is also capable of integrating the wave propagation problems on much larger time intervals than was previously possible.