A New Newton-Type Method with Third-Order for Solving Systems of Nonlinear Equations

Abstract

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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