Application of a Chebyshev Collocation Method to Solve a Parabolic Equation Model of Underwater Acoustic Propagation

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.