Symbolic-Numerical Implementation of the Galerkin Method for Approximate Solution of the Waveguide Diffraction Problem

In this paper, we construct a symbolic-numerical implementation of the Galerkin method for approximate solution of the waveguide diffraction problem at the junction of two open planar three-layer waveguides. The Gelerkin method is implemented in the <span class="u-monospace">Maple</span> computer algebra system by symbolic manipulations; its software implementation is based on the <span class="u-monospace">scprod</span> symbolic-numerical procedure, which enables the numerical calculation of scalar products for the Galerkin method based on symbolic expressions. The use of symbolic manipulations makes it possible to speed up the calculation of integrals in the Galerkin method owing to single-run symbolic calculation of integrals typical for the problem, rather than multiple numerical integration.