Systematic solution of nonlinear equations with close or double roots in complex domain: Application of SCVS algorithm for crosswise complex dispersion characteristics

This paper shows the application of Simplex Search Vertices Searching (SCVS) algorithm in solving nonlinear equations of the form F(f, γ) = 0, where f ϵ ℝ, γ ϵ C and F is complex function, for the case where we face the problem of close or double complex roots. This problem is solved with the use of standard SCVS procedure, recently reported. In this case 2- and 3-Simplexes are used for root tracking routine. Analyzing the sign of function F at the vertices of considered simplexes we can infer whether there is one or two roots in its volume. Numerical results of calculating dispersion characteristics, for selected ferrite line, are shown to prove the performance of the proposed method.