The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.
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Dmitriy Divakov, Mikhail Malykh, Leonid Sevastianov, Anton Sevastianov, Anastasiia Tiutiunnik, "The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type," Proc. SPIE 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III, 103370G (14 April 2017);