Rational approximations to \(1/ \sqrt {1-s^ 2}\), one-way wave equations and absorbing boundary conditions (Q1923456)

One-way wave equations (OWWEs), derived from rational approximations \(C(s)\) to \(1/\sqrt{1-s^2}\) are considered. Absorbing boundary conditions obtained from these OWWEs are easily implemented, producing systems of differential equations at the boundary. These equations are different from those obtained by rational approximations \(r(s)\) to \(\sqrt{1-s^2}\). However a particular choice of difference approximation for the system yields numerical methods such that stability properties of both approaches are equivalent. Numerical results are presented which demonstrate that in some cases the \(C(s)\) OWWEs can provide better absorption.