Abstract
A numerical algorithm that can quantitatively solve transcendental equation sets with multiple independent variables in the complex number domain is presented in this paper. A strict mathematical proof of solving the unary transcendental equation in the real domain is given in detail to show the process of the algorithm, which can be generalized to the equations with two or more variables. The complex variable concerned in this method is treated as two independent variables in real domain that represent the real part and the imaginary part of the variable, respectively. The criterion for choosing the dimension of scanning elements is given to overcome the difficulty in solving the general multivariate equation. Finally, the algorithm is applied in the problem of plotting 3-D dispersion curves in complex wave number and real frequency domains. Three examples are used to illustrate the correctness and effectiveness of the algorithm.
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