A e s r r u c r AND iNTRODUCTlON Convergence is an often used but rarely defined concept. Ideas such as the creation of synergies, disappearance of industry boundaries, integration, or overlapping of markets, are all used to describe this phenomenon. Where is convergence occurring and what effects has this phenomenon for the industries involved? We give an overview of the current competition an...

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 control the first moment of the initial approximations and obtain the order of convergence and the asymptotic profile of a general solution by two explicit “canonical” approximations: a diffusive N-wave and a diffusion wave solution. The order of convergence of both approximations is O(t1/(2r)−3/2) in Lr norm, 1 ≤ r ≤ ∞, as t → ∞, which is faster than the well-known classical c...

An improved iterative method of Euler’s type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of fourth order, Carstensen-Petković’s approach [7] using Weierstrass’ correction is applied. It is proved that the R-order of convergence of the improved Euler-like method is (asymptotically) 2 + √ 7 ≈ 4.646 or 5, depending of the type...

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 ...

‎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...