Solve nonlinear equation systems using midpoint Newton method

Abstract

This article discusses a Midpoint Newton method for solve nonlinear equations system. This method has a cubic convergence order, therefore it converges faster than the Newton method, which has a quadratic convergence order. Solving nonlinear systems using the methods began with finding a system solution for nonlinear equations through Newton's method. The value of the solution was substituted into the Midpoint Newton method. Iteration stoped if the iteration error was smaller than the tolerance error given. Numerical computation has been given to shown that Midpoint Newton method enabled to solve some examples of nonlinear equation systems.