One-way large range step methods for Helmholtz waveguides (Q1306111)

For long range computation of the Helmholtz equation in a waveguide it is useful to reformulate it as the differential Riccati equation for the Dirichlet-to-Neumann map. For waveguides with slow range dependence, the piecewise range-independent approximation is used to derive a second-order range stepping method. The author develops a fourth-order method for the one-way reformulation. Numerical examples demonstrate the unproved accuracy of the method.