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...

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ p=1 $p=\infty$ prove that both Caputo Fabrizio is a positive real r, 0<r<1. Finally, compare speed between obtaining they related Digamma function.

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...

in this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. periteration this method requires three evaluations of the function and one evaluation of its first derivative. a general error analysis providing the eighth order of convergence is given. several numerical examples are given to illustrate the efficiency and performance of the new ...

A general class of three-point iterative methods for solving nonlinear equations is constructed. Its order of convergence reaches eight with only four function evaluations per iteration, which means that the proposed methods possess as high as possible computational efficiency in the sense of the Kung-Traub hypothesis (1974). Numerical examples are included to demonstrate a spectacular converge...

‎in this paper‎, ‎we present a new modification of chebyshev-halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎the convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎so‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that o...