The parabolic approximation has been used extensively for underwater acoustic propagation and is attractive because it is computationally efficient. Widely used parabolic equation (PE) model programs such as the range-dependent acoustic model (RAM) are discretized by the finite difference method. Based on the idea of the Pad\(\acute{\text {e}}\) series expansion of the depth operator, a new discrete PE model using the Chebyshev collocation method (CCM) is derived, and the code (CCMPE) is developed. Taking the problems of four ideal fluid waveguides as experiments, the correctness of the discrete PE model using the CCM to solve a simple underwater acoustic propagation problem is verified. The test results show that the CCMPE developed in this article achieves higher accuracy in the calculation of underwater acoustic propagation in a simple marine environment and requires fewer discrete grid points than the finite difference discrete PE model. Furthermore, although the running time of the proposed method is longer than that of the finite difference discrete PE program (RAM), it is shorter than that of the Chebyshev–Tau spectral method.

抛物线近似已经广泛用于水下声传播，并且由于其计算效率高而具有吸引力。通过有限差分法离散了广泛使用的抛物线方程（PE）模型程序，例如与范围相关的声学模型（RAM）。基于Pad \（\ acute {\ text {e}} \）的想法通过深度算子的级数展开，推导了使用切比雪夫搭配法（CCM）的新离散PE模型，并开发了代码（CCMPE）。以四个理想的流体波导问题为实验，验证了利用CCM解决简单的水声传播问题的离散PE模型的正确性。测试结果表明，本文开发的CCMPE在简单海洋环境中的水下声传播计算中具有更高的精度，并且与有限差分离散PE模型相比，需要的离散网格点更少。此外，尽管该方法的运行时间比有限差分离散PE程序（RAM）的运行时间长，但比Chebyshev-Tau谱方法的运行时间短。