A New Non-Divergent Root Finding Algorithm (Journal of Informatics and Mathematical Sciences, 2025)
A new iteration algorithm is proposed. The algorithm does not diverge when the first derivative is zero or nearly zero as in the case of Newton-Raphson method. The convergence rate of the new algorithm is linear compared to the quadratic convergence of the Newton-Raphson method (The Newton-Raphson method is faster). The algorithm significantly increases the interval of convergence for roots. A hybrid algorithm combining the increase in the range of convergence of the new method and the faster rate of convergence of the Newton-Raphson method is suggested. The criterion to select the best choice during the running of the algorithm is given. Numerical examples are treated and the three methods (Non-Divergent Algorithm, Newton-Raphson method and the Hybrid method) are contrasted with each other. The hybrid method is recommended since it decreases the number of iterations and increases the range of convergence.