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

Applying the Chebyshev-Tau spectral method to solve the parabolic equation model of wide-angle rational approximation in ocean acoustics