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One-way large range step methods for Helmholtz waveguides. (English) Zbl 0944.65110
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.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
78A50 Antennas, waveguides in optics and electromagnetic theory
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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