文献类型：期刊文献

中文题名：A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

英文题名：A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

作者：Zhongli Liu[1];Quanyou Fang[1]

第一作者：刘忠礼

机构：[1]College of Biochemical Engineering, Beijing Union University, Beijing, China

第一机构：北京联合大学生物化学工程学院

年份：2015

卷号：3

期号：10

起止页码：1256-1261

中文期刊名：应用数学与应用物理（英文）

语种：英文

中文关键词：Newton-Type;Method;Systems;of;Nonlinear;Equations;Third-Order;Convergence;Integral;Interpolation

外文关键词：Newton-Type Method;Systems of Nonlinear Equations;Third-Order Convergence;Integral Interpolation

摘要：In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.
In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.