[PDF] Top 20 A Class of Iterative Methods for Solving Nonlinear Equations with Optimal Fourth order Convergence

... In this section we give some physical examples and compare our methods with other some well known methods. Here all the computations have been done by using Mathematica 8. We consider the number of decimal ... 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

... 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

... being developed using several different techniques including Taylor series, quadrature formu- las, homotopy and decomposition techniques, see [ 1, 2, 4, 7, 9-16 ] and the references therein. There are several different ... See full document

... variable nonlinear equation (1) efficiently, is an interesting very old problem in numerical analysis and has many applications in applied ...many iterative methods for solving ... See full document

... approximate methods to solve such algebraic and transcendental ...of nonlinear equations are difficult to solve in ...these equations is by iterative ...classical methods to ... See full document

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

... use iterative methods such as Newton’s method [1,2] and its variants namely, Halley’s method [1-6], Chebyshev’s method [1-6], Chebyshev-Halley type methods [6] ...the convergence of Newton’s ... See full document

... proposed fourth-order methods converge more rapidly than Newton’s method and require the less num- ber of function evaluations, so that they can compete with Newton’s ...new methods have at ... See full document

... –step iterative method without second derivative was suggested for finding roots of nonlinear ...the convergence is performed to show that the convergence order of the new method is ... See full document

... adaptive methods with memory in this ...general optimal multi- point method without memory, using n + 1 func- tional evaluations has optimal convergence order 2 n , so it could reach ... See full document

... of iterative methods for solving non-linear equations and prove that the order of convergence of these methods is at least ...new methods require two evaluations of ... See full document

... in order to address optimization problems ...particular class of evolutionary algorithms that apply a local search in order to refine the current approximation of the global ... See full document

... 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 computational ... 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

... In the section 2 of this paper, we develop an iterative method for solving (1.1) and its convergence criteria is discussed. And also, few variants are derived from this new method in the same ... See full document

... 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

... derivative-free methods for solving nonlinear equations is ...these methods have the convergence order of ...new methods are derivative-free and only use four ... 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. To check ... See full document

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