Bernardi, Christine; Pelissier, Marie-Claude Spectral discretization of a mixed Schrödinger boundary value problem and application. (English) Zbl 0812.76058 Finite Elem. Anal. Des. 16, No. 3-4, 309-315 (1994). Summary: Paraxial approximation to the Helmholtz equation in ocean acoustics leads to solving a mixed Schrödinger boundary value problem. The numerical analysis is performed combining a spectral method in the depth direction and a leap-frog scheme in the propagation direction. A convergence analysis for the approximation is developed, providing error estimates. MSC: 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76Q05 Hydro- and aero-acoustics 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 86A05 Hydrology, hydrography, oceanography Keywords:Helmholtz equation; ocean acoustics; leap-frog scheme; convergence; error estimates PDFBibTeX XMLCite \textit{C. Bernardi} and \textit{M.-C. Pelissier}, Finite Elem. Anal. Des. 16, No. 3--4, 309--315 (1994; Zbl 0812.76058) Full Text: DOI