TITLE:
Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs
AUTHORS:
Zhongli Liu, Guoqing Sun
KEYWORDS:
Iterative Method, Gauss-Legendre Quadrature Formula, Nonlinear Systems, Third-Order Convergence, Nonlinear ODEs
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.11,
November
18,
2016
ABSTRACT: 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.