A Family Third-order Methods with One Parameter for Solving Systems of Nonlinear Equations and BVP-ODEs

Abstract

Efficient numerical solutions for systems of nonlinear equations have always appealed greatly to people in scientific computation and engineering fields. And how to make the two iterative approximate values as precise as possible is an important issue in actual computation. In this paper, we use the linear-combination method to construct a family third-order scheme with one parameter for solving systems of nonlinear equations. Their cubic convergence and corresponding error equation are proved theoretically, and numerical examples are demonstrated as well to show the efficiency and feasibility of the suggested iterative methods.