The Riccati method for sound propagation in ocean

The Riccati equation for the Dirichlet-to-Neumann map is derived from the exact factorization of the two dimensional variable coefficient Helmholtz equation. A numerical scheme is developed for the Riccati equation based on a local eigenfunction expansion. The efficiency and accuracy of the method is demonstrated by numerical experiments including the plane-parallel range-dependent waveguide benchmark problem proposed by the Acoustical Society of America.