[PDF] Top 20 Improving the convergence order and efficiency index of quadrature-based iterative methods for solving nonlinear equations

... 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 ... See full document

... new methods that are iterative based, is to develop methods that can attain optimal convergence requiring few number of functions and derivatives evaluations in an iteration ...the ... See full document

... build iterative methods of optimal higher order of ...the methods in which (first, second, ...eighth-order iterative method to find a simple root α of the nonlinear equation ... See full document

... adaptive methods with memory in this ...best efficiency index which comes from the point of the efficiency in- ...optimal convergence order 2 n , so it could reach the optimal ... See full document

... step iterative methods free derivative to solve a nonlinear ...new iterative method free derivative has four order of convergence and four evaluations of the function per ... See full document

... the methods with the highest computational order of ...our methods with other optimal sixteenth order ...more nonlinear functions and find the best member based on the highest ... See full document

... three-step quadrature based iterative methods with sixth, seventh and eight order of conver- gence for finding simple zeros of nonlinear ...three-step iterative ... See full document

... new iterative methods for approximating the solution of (1) has attracted the attention of researchers in recent years, as evident in the li- terature such as [9] [10] [11] ...developing iterative ... See full document

... two-stepweight iterative methods based on series expansion of nonlinear ...the methods are of order three convergences. The methods and their algorithms are in section ... See full document

... new iterative methods of order four and five for the solution of nonlinear equations based on homotopy perturbation ...technique. Convergence analysis is also discussed. ... See full document

... iteration methods, without memory based on n evaluations, could achieve optimal convergence order 2 n−1 ...derivative-free methods which agree with the Kung and Traub conjecture for n ... See full document

... –order iterative method obtained by Rostom and Fuad ...–order iterative method for solving nonlinear ...steps based on Newton equation , finite difference method and ... See full document

... numerical iterative methods have been suggested and analyzed under certain ...to iterative methods are order of convergence and computational ...The efficiency ... See full document

... Many iterative methods have been developed see [1-13] for solving the equation ...perturbation methods and quadrature ...fourth order convergence ... See full document

... third-order iterative method for solving nonlinear equations for simple roots by using inverse function ...fourth-order methods by using one function and two first ... See full document

... new iterative methods for solving nonlinear equations are presented using a new quadrature rule based on spline ...of convergence shows that these methods ... See full document

... The nonlinear equations, often arise from the numerical modeling of problems in many branches of science and engineering ...These equations more often are not solved analytically hence resort to ... See full document

... multi-step iterative methods with the improved convergence order, see [12], ...convergent iterative methods [29], ...sixth-order methods by weight func- tion ... See full document

... three-step iterative method for solving nonlinear ...third order of convergence and an improvement to previous ...the order of convergence of the previous scheme is two, ... See full document

... Steffensen-type methods were derived in the literature (see ...Steffensen-type methods and their applications in the solution of nonlinear systems and nonlinear differential equations ... See full document