Wide-angle mode parabolic equation with transparent boundary conditions and its applications in shallow water acoustics

A wide-angle mode parabolic equation is obtained from the horizontal refraction equation by using the rational-linear approximation of the square-root operator. A finite-difference scheme for the numerical solution of the derived equation is developed. The scheme is based on the standard Crank–Nicolson method and fully-discrete transparent boundary conditions which allow for an accurate simulation of sound propagation on an unbounded domain.