Article

A composite third order Newton–Steffensen method for solving nonlinear equations

Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148 106 District Sangrur, India
Applied Mathematics and Computation (Impact Factor: 1.55). 10/2005; 169(1):242-246. DOI: 10.1016/j.amc.2004.10.040
Source: DBLP

ABSTRACT

In this paper, we suggest a third-order method formed by the composition of Newton and Steffensen methods for finding simple and real roots of a nonlinear equation in single variable. Per iteration the formula requires two evaluations of the function and single evaluation of the derivative. Experiments show that the method is suitable in the cases where Newton and Steffensen methods fail.

  • Source
    • "The major drawback of offered schemes is that, for corrector step of these methods, computation of the second derivative is necessary, which most of the time is excessively difficult. There have been many attempts in the literature to overcome aforementioned shortcoming for improving these methods by making relevant algorithms free from the second derivatives [3] [4] [5]. It is shown that the rate of convergence of the modified iterative methods varies according to operation of various parameters [6] [7]. "

    Full-text · Dataset · May 2015
  • Source
    • "The major drawback of offered schemes is that, for corrector step of these methods, computation of the second derivative is necessary, which most of the time is excessively difficult. There have been many attempts in the literature to overcome aforementioned shortcoming for improving these methods by making relevant algorithms free from the second derivatives [3] [4] [5]. It is shown that the rate of convergence of the modified iterative methods varies according to operation of various parameters [6] [7]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents an efficient iterative method originated from the family of Chebyshev’s operations for the solution of nonlinear problems. For this aim, the product operation matrix of integration is presented, and therefore the operation of derivative is developed by using Chebyshev wavelet functions of the first and second kind, initially. Later, Chebyshev’s iterative method is improved by approximation of the first and second derivatives. The analysis of convergence demonstrates that the method is at least fourth-order convergent. The effectiveness of the proposed scheme is numerically and practically evaluated. It is concluded that it requires the less number of iterations and lies on the best performance of the proposed method, especially for highly varying nonlinear problems.
    Full-text · Article · Mar 2015 · Mathematical Problems in Engineering
  • Source
    • "In the last decade, several iterative methods have been developed to improve the traditional Newton–Raphson method [Petkovic and Petkovic (2010); Babajee and Dauhoo (2006); Chun (2006)]. In most proposed methods, the evaluation of the second derivatives is not necessary [Chun (2007); Sharma (2005); Noor and Noor (2006)]. In this study, a new family of eighth order iterative methods for nonlinear analysis of structures has been developed. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a new approach is presented to accelerate the nonlinear analysis of structures with low computational cost. The method is essentially based on Newton–Raphson method, which has been improved in each iteration to achieve faster convergence. The normal flow algorithm has been employed to pass successfully through the limit points and through the entire equilibrium path. Subsequently, numerical examples are performed to demonstrate the efficiency of the formulation. The results show better performance, accuracy and rate of convergence of the present method to deal with nonlinear analysis of structures.
    Full-text · Article · Aug 2013 · International Journal of Computational Methods
Show more