Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs  

作　　者：Zhongli Liu Guoqing Sun Zhongli Liu;Guoqing Sun(College of Biochemical Engineering, Beijing Union University, Beijing, China;College of Renai, Tianjin University, Tianjin, China)

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

出　　处：《Journal of Applied Mathematics and Physics》2016年第11期2038-2046,共9页应用数学与应用物理（英文）

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.

关 键 词：Iterative Method Gauss-Legendre Quadrature Formula Nonlinear Systems Third-Order Convergence Nonlinear ODEs 

分 类 号：O17[理学—数学]