An efficient fourth order weighted‐Newton method for systems of nonlinear equations

In this paper, we develop a fourth order method for solving the systems of nonlinear equations. The algorithm is composed of two weighted‐Newton steps and requires the information of one function and two first Fréchet derivatives. Therefore, for a system of n equations, per iteration it uses n + 2n ² evaluations. Computational efficiency is compared with Newton’s method and some other recently published methods. Numerical tests are performed, which confirm the theoretical results. From the comparison with known methods it is observed that present method shows good stability and robustness.