A Modified Fixed-Newton’s Method Via Mid-Point Approach for Nonlinear Systems of Equations

Abstract

The major shortcomings of Classical Newton's method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in every iteration. Mostly function derivatives are quit costly and Jacobian is computationally expensive which requires storage of matrix in each iteration. The appealing approach is based on Fixed Newton's but the method mostly requires high number of iteration as the dimension of the systems increases due to less Jacobian information in every iteration. In this paper, we introduce a new procedure via two-step scheme that will reduce the well known shortcomings of Fixed and classical Newton methods. Numerical experiments are carried out which shows that, the proposed method is very encouraging are presented.