Applying the Chebyshev–Tau Spectral Method to Solve the Parabolic Equation Model of Wide-Angle Rational Approximation in Ocean Acoustics

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