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Spectral discretization of a mixed Schrödinger boundary value problem and application. (English) Zbl 0812.76058

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
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