论文信息 - A Fourth-Order Newton-Type Method Free from Second Derivative for Solving Non-linear Equations

A Fourth-Order Newton-Type Method Free from Second Derivative for Solving Non-linear Equations

In this paper, we present a class of third-order Newton-type methods for solving non-linear equations by considering linear combination of two well-known third-order methods. Based on this, we obtain a fourth-order convergent method. The proposed approach is free from second derivatives. In each step, it only requires two evaluations of the given function and one evaluation of its first derivative. Analysis of efficiency demonstrates that the algorithm is superior and performs well.

Wei Zhang | Xiaoyan Ma | Liang Fang | Zhongyong Hu

[1] M. V Mederos,et al. Gautschi, Walter. Numerical analysis: an introduction, Birkhäuser, 1997 , 1999 .

[2] W. Gautschi. Numerical analysis: an introduction , 1997 .

[3] Changbum Chun,et al. A simply constructed third-order modifications of Newton's method , 2008 .

[4] Guoping He,et al. Some modifications of Newton's method with higher-order convergence for solving nonlinear equations , 2009 .

[5] Muhammad Aslam Noor,et al. Fourth-order convergent iterative method for nonlinear equation , 2006, Appl. Math. Comput..

[6] Guoping He,et al. A cubically convergent Newton-type method under weak conditions , 2008 .

[7] Guoping He,et al. An efficient Newton-type method with fifth-order convergence for solving nonlinear equations , 2008 .

[8] Jisheng Kou,et al. The improvements of modified Newton's method , 2007, Appl. Math. Comput..