  Solving an acoustic wave equation using a parabolic approximation is a
popular approach for many existing ocean acoustic models. Commonly used
parabolic equation (PE) model programs, such as the range-dependent acoustic
model (RAM), are discretized by the finite difference method (FDM). Considering
the idea and theory of the wide-angle rational approximation, a discrete PE
model using the Chebyshev spectral method (CSM) is derived, and the code is
developed. This method is currently suitable only for range-independent
waveguides. Taking three ideal fluid waveguides as examples, the correctness of
using the CSM discrete PE model in solving the underwater acoustic propagation
problem is verified. The test results show that compared with the RAM, the
method proposed in this paper can achieve higher accuracy in computational
underwater acoustics and requires fewer discrete grid points. After
optimization, this method is more advantageous than the FDM in terms of speed.
Thus, the CSM provides high-precision reference standards for benchmark
examples of the range-independent PE model.
