A new fourth-order iterative method for finding multiple roots of nonlinear equations
نویسندگان
چکیده
In th is paper, we present a fifth-order method for find ing mult iple zeros of nonlinear equations. Per iteration, the new method requires two evaluations of functions and two of its first derivative. It is proved that the method has a convergence of order five. Finally, some numerical examples are g iven to show the performance of the presented method, and compared with some known methods.
منابع مشابه
THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS
In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
متن کاملA Third Order Iterative Method for Finding Zeros of Nonlinear Equations
In this paper, we present a new modification of Newton's method for finding a simple root of a nonlinear equation. It has been proved that the new method converges cubically.
متن کاملNew iterative methods with seventh-order convergence for solving nonlinear equations
In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.
متن کاملA new optimal method of fourth-order convergence for solving nonlinear equations
In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...
متن کاملSome fourth-order nonlinear solvers with closed formulae for multiple roots
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Newton's method Multiple roots Nonlinear equations Iterative methods Root finding a b s t r a c t In this paper, w...
متن کاملA Three-Point Iterative Method for Solving Nonlinear Equations with High Efficiency Index
In this paper, we proposed a three-point iterative method for finding the simple roots of non- linear equations via mid-point and interpolation approach. The method requires one evaluation of the derivative and three(3) functions evaluation with efficiency index of 81/4 ≈ 1.682. Numerical results reported here, between the proposed method with some other existing methods shows that our method i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Mathematics and Computation
دوره 215 شماره
صفحات -
تاریخ انتشار 2009