• 论文 •

### 三步五阶迭代方法解非线性方程组

1. 合肥工业大学数学学院, 合肥 230009
• 收稿日期:2012-12-25 出版日期:2013-08-15 发布日期:2013-09-07
• 基金资助:

国家自然科学基金-广东联合基金重点项目(U1135003);国家自然科学基金项目(61070227)

Zhang Xu, Tan Jieqing. THE FIFTH ORDER OF THREE-STEP ITERATIVE METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS[J]. Mathematica Numerica Sinica, 2013, 35(3): 297-304.

### THE FIFTH ORDER OF THREE-STEP ITERATIVE METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Zhang Xu, Tan Jieqing

1. School of Mathematics, Hefei University of Technology, Hefei 230009, China
• Received:2012-12-25 Online:2013-08-15 Published:2013-09-07

In this paper, we present and analyze three new three-step iterative methods for solving the system of nonlinear equations using quadrature formulas. We prove that these new methods are of the convergence of fifth order. Some numerical examples are given to show that the new methods outperform the other existing methods.

MR(2010)主题分类:

()
 [1] Sharma J R, Guha R K, Sharma R. An efficient fourth order weighted-Newton method for systems of nonlinear equations[J]. Numerical Algorithms, 2013, 62(2): 307-323. [2] Golbabai A, Javidi M. A new family of iterative methods for solving system of nonlinear algebric equations[J]. Applied Mathematics and Computation, 2007, 190(2): 1717-1722. [3] Darvishi M T, Barati A. Super cubic iterative methods to solve systems of nonlinear equations[J]. Applied Mathematics and Computation, 2007, 188(2): 1678-1685. [4] Babajee D K R, Dauhoo M Z, Darvishi M T, Barati A. A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule[J]. Applied Mathematics and Computation, 2008, 200(1): 452-458. [5] Khirallah M Q, Hafiz M A. Novel three order methods for solving a system of nonlinear equations[J]. Bulletin of Society for Mathematical Services and Standards, 2012, 1(2): 1-14. [6] Hafiz M A, Bahgat M S M. An efficient two-step iterative method for solving system of nonlinear equations[J]. Journal of Mathematics Research, 2012, 4(4): 28-34. [7] Cordero A, Torregrosa J R. Variants of Newton's method using fifth-order quadrature formulas[J]. Applied Mathematics and Computation, 2007, 190(1): 686-698. [8] Noor M A, Waseem M. Some iterative methods for solving a system of nonlinear equations[J]. Computers and Mathematics with Applications, 2009, 57(1): 101-106. [9] 代璐璐, 檀结庆. 两种解非线性方程组的四阶迭代方法[J]. 数值 计算与计算机应用, 2012, 33(2): 121-128. [10] Ortega J M, Rheinboldt W C. Iterative solution of nonlinear equations in several variables[M]. New York and London: Academic Press, 1970. [11] Podisuk M, Chundang U, Sanprasert W. Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation[J]. Applied Mathematics and Computation, 2007, 190(2): 1438-1444. [12] Cordero A, Hueso J L, Martínez E, Torregrosa J R. Increasing the convergence order of an iterative method for nonlinear systems[J]. Applied Mathematics Letters, 2012, 25(12): 2369-2374. [13] Cordero A, Hueso J L, Martínez E, Torregrosa J R. A modified Newton-Jarratt's composition[J]. Numerical Algorithms, 2010, 55(1): 87-99. [14] 何翠杰, 阿布都热西提·阿布都外力. 三步迭代求解非线 性方程组[J]. 新疆大学学报: 自然科学版, 2010, 27(1): 51-55.
 [1] 马积瑞, 范金燕. 信赖域方法在Hölderian局部误差界下的收敛性质[J]. 计算数学, 2021, 43(4): 484-492. [2] 高兴华, 李宏, 刘洋. 分布阶扩散—波动方程的有限元解的误差估计[J]. 计算数学, 2021, 43(4): 493-505. [3] 刘金魁, 孙悦, 赵永祥. 凸约束伪单调方程组的无导数投影算法[J]. 计算数学, 2021, 43(3): 388-400. [4] 王同科, 樊梦. 第二类端点奇异Fredholm积分方程的分数阶退化核方法[J]. 计算数学, 2019, 41(1): 66-81. [5] 裕静静, 江平, 刘植. 两类五阶解非线性方程组的迭代算法[J]. 计算数学, 2017, 39(2): 151-166. [6] 张旭, 檀结庆, 艾列富. 一种求解非线性方程组的3p阶迭代方法[J]. 计算数学, 2017, 39(1): 14-22. [7] 郭俊, 吴开腾, 张莉, 夏林林. 一种新的求非线性方程组的数值延拓法[J]. 计算数学, 2017, 39(1): 33-41. [8] 许秀秀, 黄秋梅. 拟等级网格下非线性延迟微分方程间断有限元法[J]. 计算数学, 2016, 38(3): 281-288. [9] 樊梦, 王同科, 常慧宾. 非光滑函数的分数阶插值公式[J]. 计算数学, 2016, 38(2): 212-224. [10] 张英晗, 杨小远. 一类带有空间时间白噪音随机弹性方程的全离散差分格式[J]. 计算数学, 2016, 38(1): 25-46. [11] 孟文辉, 王连堂. Helmholtz方程周期Green函数及其偏导数截断误差收敛阶的分析[J]. 计算数学, 2015, 37(2): 123-136. [12] 刘晴, 檀结庆, 张旭. 一种基于Chebyshev迭代解非线性方程组的方法[J]. 计算数学, 2015, 37(1): 14-20. [13] 王洋, 伍渝江, 付军. 一类弱非线性方程组的Picard-MHSS迭代方法[J]. 计算数学, 2014, 36(3): 291-302. [14] 杨爱利, 伍渝江, 李旭, 孟玲玲. 一类非线性方程组的Newton-PSS迭代法[J]. 计算数学, 2012, 34(4): 329-340. [15] 陈传淼, 胡宏伶, 雷蕾, 曾星星. 非线性方程组的Newton流线法[J]. 计算数学, 2012, 34(3): 235-258.