  The stepwise coupled-mode model is a classic approach for solving
range-dependent sound propagation problems. Existing coupled-mode programs have
disadvantages such as high computational cost, weak adaptability to complex
ocean environments and numerical instability. In this paper, a new algorithm is
designed that uses an improved range normalization and global matrix approach
to address range dependence in ocean environments. Due to its high accuracy in
solving differential equations, the spectral method has recently been applied
to range-independent normal modes and has achieved remarkable results. This
algorithm uses the Chebyshev--Tau spectral method to solve for the eigenmodes
in the range-independent segments. The main steps of the algorithm are
parallelized, so OpenMP multithreading technology is also applied for further
acceleration. Based on this algorithm, an efficient program is developed, and
numerical simulations verify that this algorithm is reliable, accurate and
capable. Compared with the existing coupled-mode programs, the newly developed
program is more stable and efficient at comparable accuracies and can solve
waveguides in more complex and realistic ocean environments.
