One class of waveguide resonators: algorithms based on semi-inversion technique in time and frequency domain

Abstract

An approach, based on extraction and analytical inversion of the singular part of the boundary value problem (BVP) operator in the frequency and time domain is applied to the one class of resonant structures in waveguides (coaxial type plane discontinuities bifurcation's, shunts, slots, irises, steps, disks etc.). Thus the initial BVP and BVP are reduced to the matrix equation of the second kind or to the Volterra integral equation of the second kind (with a straightforward scheme of time marching). All steps of the technique are mathematically proved. The convergence of numerical algorithms is proved also and estimated analytically. Special attention is paid to computer implementation of algorithms developed and various tests of them. Thus the convergence of numerical solutions is thoroughly investigated and analytical estimates are illustrated by numerical results.