Author(s)

Zhongli Liu^1*, Guoqing Sun²

¹College of Biochemical Engineering, Beijing Union University, Beijing, China.
²College of Renai, Tianjin University, Tianjin, China.

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.

Iterative Method, Gauss-Legendre Quadrature Formula, Nonlinear Systems, Third-Order Convergence, Nonlinear ODEs

Liu, Z. and Sun, G. (2016) Gauss-Legendre Iterative Methods and Their Applications on Nonlinear Systems and BVP-ODEs. Journal of Applied Mathematics and Physics, 4, 2038-2046. doi: 10.4236/jamp.2016.411203.