AN IMPROVED ITERATIVE SCHEME FOR REAL AND COMPLEX ROOTS DETECTION

In this study, researchers propose an innovative numerical approach to solve non-linear equations for real as well as complex roots. The approach, initiated with an initial guess in the complex plane, iteratively converges towards solutions. A notable feature is its ability to accurately identify complex roots even when initialized with a real number. The method demonstrates second-order convergence, with its efficacy evaluated through quantifying the number of iterations needed for convergence. Using Python 3.10.9, experiments were conducted to evaluate its effectiveness across various numerical problems. Results were presented in tabular format, supplemented by graphical representations. Furthermore, the study examines the method's computational efficiency by analyzing CPU time and introducing an efficiency index.