Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

There is no doubt that the fourth-order King’s family one of important ones among its counterparts. However, it has two major problems: first calculation first-order derivative; secondly, a linear order convergence in case multiple roots. In to improve these complications, we suggested new iterative methods. The main features our scheme are optimal order, being free from derivatives, and working for roots (m≥2). addition, proposed theorem illustrated fourth convergence. It also satisfied Kung–Traub conjecture methods without memory. We compared with latest same on several real-life problems. accordance computational results, concluded method showed superior behavior existing