Ultraconveniently Finding Multiple Solutions of Complex Transcendental Equations Based on Genetic Algorithm

Abstract

Getting all multiple solutions of complex transcendental equations is very important in scientific computing. A new and effective algorithm combining Genetic Algorithm (GA) with Parameter Tracking Scheme (PTS) and Dynamic Searching Area (DSA) is developed. By using the algorithm, the rooting problem of all kinds of complex and transcendental equations in electromagnetic field can be solved successfully, such as the eigenvalue equation of surface wave of microstrip antenna fed with coaxial line, the complex transcendental equation of medium permittivity that is measured by the method of terminal short circuit, and the characteristic equation of rectangular waveguide that is filled partially by magnetic materials and so forth. The computing results have good agreements with known outcomes of these questions obtained by other methods, for instance, Kuhn algorithm and iterative method. As compared with other schemes, the algorithm has some advantages, such as initial value and gradient information free, completeness, robustness, generalization, and precision etc.