文献类型：期刊文献

中文题名：Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

英文题名：Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs

作者：Zhongli Liu[1];Guoqing Sun[2]

第一作者：刘忠礼

机构：[1]College of Biochemical Engineering, Beijing Union University, Beijing, China;[2]College of Renai, Tianjin University, Tianjin, China

第一机构：北京联合大学生物化学工程学院

年份：2016

卷号：4

期号：11

起止页码：2038-2046

中文期刊名：应用数学与应用物理（英文）

外文期刊名：Journal of Applied Mathematics and Physics

语种：英文

中文关键词：Iterative Method;Gauss-Legendre Quadrature Formula;Nonlinear Systems;Third-Order Convergence;Nonlinear ODEs

外文关键词：Iterative Method;Gauss-Legendre Quadrature Formula;Nonlinear Systems;Third-Order Convergence;Nonlinear ODEs

摘要：In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.
In this paper, a group of Gauss-Legendre iterative methods with cubic convergence for solving nonlinear systems are proposed. We construct the iterative schemes based on Gauss-Legendre quadrature formula. The cubic convergence and error equation are proved theoretically, and demonstrated numerically. Several numerical examples for solving the system of nonlinear equations and boundary-value problems of nonlinear ordinary differential equations (ODEs) are provided to illustrate the efficiency and performance of the suggested iterative methods.