EIGENVALUE COMPUTATION FOR APPLICATION OF THE FINITE HANKEL TRANSFORM IN COAXIAL REGIONS - Delecki, Z. A. (Applied Computational Electromagnetics Society Journal (ACES), 2022)
The evaluation of eigenvalues for transcendental equations in the cylindrical coordinate system is considered. A new code has been developed for this purpose. This is a fast algorithm for finding contours of a real function of two variables. This algorithm searches for the interval in which the function passes through the desired reference value and subsequently automatically starts to trace the contour within a circular annulus region of interest. When the reference value is zero and the function represents the limiting form of the Finite Hankel Transform kernel, the solution of the transcendental equation for eigenvalues is obtained. For accurate values of proper numbers, another code provides them with the desired uncertainty. Numerical results are presented and compared with available data. The computed eigenvalues may be used to obtain solutions of boundary value problems for circularly-symmetric electromagnetic waveguides, cables, cavities or scatterers. [Vol. 4, No. 1, pp. 41-56 (1989)]