Author(s)

Zhongli Liu^*, Quanyou Fang

College of Biochemical Engineering, Beijing Union University, Beijing, China.

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.

Newton-Type Method, Systems of Nonlinear Equations, Third-Order Convergence, Integral Interpolation

Liu, Z. and Fang, Q. (2015) A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations. Journal of Applied Mathematics and Physics, 3, 1256-1261. doi: 10.4236/jamp.2015.310154.