title: Wide-angle one-way wave equations.
abstract: A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].
authors.affiliation: Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France.
authors.forename: L
authors.initials: L
authors.lastname: Halpern
authors.forename: L N
authors.initials: LN
authors.lastname: Trefethen
mesh_terms: D000162:Acoustics; D008433:Mathematics