[PDF] Top 20 New iterative methods with seventh-order convergence for solving nonlinear equations

... We present some examples to illustrate the efficiency of the iterative algorithm, see Table 1. We compare the Chebyshev method (CM) (see [21]-[22]); the Halley method (HM) (see [21]-[22]); the Newton ... See full document

... some methods have been proposed and analyzed for solving nonlinear equations [1, 2, 4, 6, 7, ...These methods have been suggested by using quadrature formulas, decomposition and ... 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

... a new iterative method for solving nonlinear ...these iterative methods, we show that the nonlinear function can be approximated by a new series which can be ... See full document

... two new iterative methods of order four and five by using modified homotopy perturbation ...the convergence analysis of these iterative ...these iterative methods, ... See full document

... developing new iterative methods for the approximation of the solution of equation (1), the most important rule is to design iterative methods with improved convergence rate or ... 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

... Abstract Solving nonlinear equations is one of the most important problems in numerical analysis, and has a wide range of application in various aspects, as well as many branches of science, ... See full document

... solve nonlinear equations have many applications in science and ...our new methods with well-known methods, namely, the classical Steffensen method for its simplicity 1, 2 and recently ... See full document

... Memetic Algorithms (MAs) are computational intelligence structures combining multiple and various operators in order to address optimization problems [1]. The memetic algorithms (MAs) are inspired from genetic and ... See full document

... the order of the convergence of the method [8]. In order to approximate the order of convergence of the method we use the following ... See full document

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

... nonlinear equations. [5] It is well known that when the Jacobian of nonlinear systems is nonsingular in the neighborhood of the solution, the convergence of Newton method is guaranteed and the ... See full document

... employ New Iterative Method (NIM), developed by DaftardarGejji and Jafari [17], to solve generalized Korteweg-de Vries equations of fifth and seventh orders [18, ...and nonlinear ... See full document

... the nonlinear equation f x ( ) = 0 (or x = g x ( ) ) has simple root α ∈ I , where g x ( ) : I ⊂  →  be sufficiently smooth in the neighbourhood of the root α ... See full document

... non-linear equations. This new method is examined on various examples and results presented that the suggested method is beneficial as compare to some present methods applied to solve the same ... See full document

... In this section, some numerical test of some various multiple-root- finding methods as well as our new methods and Newton’s method are presented. All computations were done using the MAPLE 13 with ... 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

... of iterative methods with higher convergence order (more than three) by the composition of Latus and some other different ...present iterative formulas defined by ...their order ... See full document

... multipoint methods for solving nonlinear equations: a survey,” Applicable Analysis and Discrete Mathematics, ...Algebraic Equations, John Wiley & Sons, New York, NY, USA, ... See full document