eng
Science and Education Publishing
American Journal of Applied Mathematics and Statistics
2328-7292
2017-04-06
5
1
22
32
10.12691/ajams-5-1-5
AJAMS2017515
article
A Family of Combined Iterative Methods for Solving Nonlinear Equations
Shuping Chen
shupingchen@126.com
1
Youhua Qian
2
College of Mathematics, Xiamen University of Technology, xiamen 361024, P. R. China
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, 321004, P. R. China
In this article we construct some higher-order modifications of Newton's method for solving nonlinear equations, which is based on the undetermined coefficients. This construction can be applied to any iteration formula. It can be found that per iteration the resulting methods add only one additional function evaluation, their order of convergence can be increased by two or three units. Higher order convergence of our methods is proved and corresponding asymptotic error constants are expressed. Numerical examples, obtained using Matlab with high precision arithmetic, are shown to demonstrate the convergence and efficiency of the combined iterative methods. It is found that the combined iterative methods produce very good results on tested examples, compared to the results produced by the existing higher order schemes in the related literature.
http://pubs.sciepub.com/ajams/5/1/5/ajams-5-1-5.pdf
Newton's method
combined iterative methods
nonlinear equations
order of convergence
computational efficiency