A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations  

作　　者：Zhongli Liu Quanyou Fang 

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

出　　处：《Journal of Applied Mathematics and Physics》2015年第10期1256-1261,共6页应用数学与应用物理（英文）

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.

关 键 词：Newton-Type Method Systems of Nonlinear EQUATIONS THIRD-ORDER CONVERGENCE INTEGRAL INTERPOLATION 

分 类 号：O1[理学—数学]