An efficient iterative method with order five for solving nonlinear systems

Article type: Research Article

Authors: Wang, Xiao-Feng^{a; b; *} | Zhang, Tie^b | Zheng, Fu^a | Qian, Wei-Yi^a

Affiliations: [a] School of Mathematics and Physics, Bohai University, Jinzhou, Liaoning, China | [b] College of Sciences, Northeastern University, Shenyang, Liaoning, China

Correspondence: [*] Corresponding author: Xiao-Feng Wang, School of Mathematics and Physics, Bohai University, Jinzhou 121013, Liaoning, China. E-mail: [email protected].

Abstract: In this paper, we present a new iterative method of convergence order five for solving nonlinear systems. Per iteration the new method requires the evaluations of two functions, two first derivatives and one matrix inversion. The computational efficiency index is used to compare the efficiency of different methods. Numerical tests are performed, which confirm the theoretical results. From the comparison with the existing methods it is observed that the new method is more efficient in both computational efficiency and computational time.

Keywords: Iterative method, Newton's method, nonlinear systems, computational efficiency

DOI: 10.3233/JCM-140512

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 14, no. 6, pp. 363-372, 2014