Rigorous numerics for the Pekeris problem

The acoustic field in an attenuating Pekeris waveguide is the limit of the field in a waveguide that is truncated at progressively larger depths. The rate of convergence is determined based on rigorous numerics using a contraction mapping in a properly formulated norm, based on Rayleigh's theorem. Given a predetermined error, the contraction mapping formulation allows the determination of the truncation depth that is needed to obtain an approximation of the field in the waveguide with the required error. Only approximations in the truncated waveguide are used to make the error determination and not the limit.