[PDF] Top 20 Steffensen Type Method of Super Third Order Convergence for Solving Nonlinear Equations

... self-accelerating Steffensen-type methods were derived in the literature (see ...[1]-[7]). Steffensen-type methods and their applications in the solution of nonlinear systems and ... See full document

... Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes ... See full document

... non-linear equations of the general form f (x) = 0. Such equations appear in real world situations frequently while there is no closed form solution for ...of equations draw much attention to itself ... See full document

... This paper is organized as follows: in section 2, we describe the new third-order iterative method by using the concept of inverse function theorem. In the next section we optimize the method ... See full document

... convergence order of the iterative method in equation (3) is higher than that of the Newton method, its efficiency index is lower because of the involvement of six function evaluation per ... See full document

... iterative type methods have been developed by using the Taylor series, decomposition and quadrature formulae (see [1-14] and the references there- ...iterative type Halley method for solving ... See full document

... a nonlinear equation. In order to increase the order of convergence of the classical Simpson method and the fourth-order Simpson-type method, we shall introduce a ... See full document

... iterative method for solving nonlinear equations of the type f(x) = 0 having eighteenth order ...Newton’s method and extrapolated Newton’s method. This ... See full document

... the convergence speed of its methods increases with the parameter ...the convergence speed can always be improved with ...Halley’s method, which is a particular case of this family obtained for p = ... See full document

... point method without memory, using n + 1 func- tional evaluations has optimal convergence order 2 n , so it could reach the optimal efficiency in- dex E ∗ (n + 1, 2 n ) = lim n →∞ ... See full document

... Newton-Steffensen third-order method by central difference quotient, we obtain a new modification of this method free from ...the method obtained preserves their order of ... See full document

... The second type of semiconductor is represented by the dotted lines in the diagram. The potential barriers are also shown in the diagram and are represented by (B). Between the two barriers is a section of the ... See full document

... In this paper, we present an iterative algorithm for the problem based on the continued fraction interpolation method. For the general iteration scheme of n points, the algorithm constructs the n + 1th point ... See full document

... of nonlinear equations and they succeeded in enhancing the method developed by Leong et al ...the convergence analysis of our proposed ... See full document

... our third order equation with the second order differential inequality and this reduction essentially simplifies the investigation of the properties of third order differential ... See full document

... x + a¨ x + b x ˙ + h(x) = p(t,x, ˙ x, ¨ x) (1.2) and established that the boundedness of both p(t) and p(τ)dτ together with the differ- entiability of the function h guaranteed the convergence of the solutions of ... See full document

... Eighteenth Order Extrapolated Newton’s method and discuss the convergence criteria of this method in section ...this method in the concluding ... See full document

... (1.2) (n = 0, 1, 2, 3 ………) Many iterative methods have been developed see [1-13] for solving the equation (1.1) by using several techniques including perturbation methods and quadrature formulae. Noor [8] ... See full document

... From these tables, one can see that the new acceleration scheme based on quadratic finite element approximation is the most quickly convergent. The iterative number is the least, only once. Since the new method is ... See full document

... In this paper, we investigated on functional Hammerstein integro-differential equa- tions of fractional order. Here we also presented an approximate method to solve these equations. We proved ... See full document