Search

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. [ABSTRACT FROM AUTHOR]