A generalization of the split-step Padé method to the case of coupled acoustic modes equation in a 3D waveguide

The split-step Padé approach is an extremely efficient tool for the integration of pseudodifferential parabolic equations, which are widely used for the modeling of acoustic wave propagation. In this study, a generalization of this method to the case of parabolic equations with unknown vector functions is presented. Such generalization requires an algorithm for efficient numerical evaluation of a function of a matrix with differential operators as its elements. After a finite-difference discretization this algorithm reduces to the solution of several Sylvester-like problems. The generalized split-step Padé method presented here is an attractive tool for solving 3D problems of sound propagation in the ocean within the framework of coupled mode parabolic equations theory. •A method is proposed for the numerical solution of the one-way counterpart of a system of coupled Helmholtz equations.•The method is based on a generalization of the split-step Padé algorithm to the case of unknown vector functions.•The method is an attractive tool for handling many practical problems where the propagation of coupled guided modes takes place.