Finite difference method

Abstract: In this paper we present a finite‐difference method to numerically determine the normal modes for the sound propagation in a stratified ocean resting on a stratified elastic bottom. The compound matrix method is used for computing an impedance condition at the ocean–elastic bottom interface. The impedance condition is then incorporated as a boundary condition into the finite difference equations in the ocean, yielding an algebraic eigenvalue problem. For each fixed mesh size this eigenvalue problem is solved by a combination of efficient numerical methods. The Richardson mesh extrapolation procedure is then used to substantially increase the accuracy of the computation. Two applications are given to demonstrate the speed, accuracy, and efficiency of the method.