One-way large range step methods for Helmholtz waveguides.

*(English)*Zbl 0944.65110For 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.

Reviewer: Laura-Iulia Aniţa (Iaşi)

##### 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 |

##### Keywords:

one-way large range step methods; Helmholtz waveguides; Helmholtz equation; numerical examples; differential Riccati equation##### Software:

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##### References:

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