A numerical approach to calculate multivariate transcendental equations in complex domain

Abstract

A numerical approach to calculate multivariate transcendental equations in complex number domain that can be applied to solve dispersion equation is presented here. The mathematical derivations of the convergence of the moduli of the equations around null point are presented strictly, when the transcendental equation is univariate. Similar process also applies to the case when the equations are multivariate. For multivariate equations, the forms of scanning elements are chosen according to the numbers of the variables and the dimensions of the solution. To validate the proposed approach, we calculate the dispersion cures of wave propagation in an infinite piezoelectric plate. As a result, the three-dimensional dispersion curves of complex wave numbers and real frequencies are obtained correctly.