A class of three-pointmethods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski’s fourth-ordermethods and amodified Newton’s method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only fou...

Making use of last derivative approximation and weight function approach, we construct an eighth-order class of three-step methods, which are consistent with the optimality conjecture of Kung-Traub for constructing multi-point methods without memory. Per iteration, any method of the developed class is totally free from derivative evaluation. Such classes of schemes are more practical when the c...

A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conjecture. Moreover, the proposed class has an accelerator parameter with the property that it can in...

This study was designed to compare the performance of a new weight estimation strategy (Mercy Method) with 12 existing weight estimation methods (APLS, Best Guess, Broselow, Leffler, Luscombe-Owens, Nelson, Shann, Theron, Traub-Johnson, Traub-Kichen) in children from India. Otherwise healthy children, 2 months to 16 years, were enrolled and weight, height, humeral length (HL), and mid-upper arm...

The neural circuits of the hippocampus are extremely complex, with many classes of interneurons whose contributions to network dynamics and function are still unknown. Nevertheless, reduced models can provide insight into aspects of the dynamics and associated function. In this chapter, we discuss models at a variety of levels of complexity, all simple enough to probe the reasons for the behavi...

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 workin...