A New High-Order and Efficient Family of Iterative Techniques for Nonlinear Models

In this paper, we want to construct a new high-order and efficient iterative technique for solving a system of nonlinear equations. For this purpose, we extend the earlier scalar scheme [16] to a system of nonlinear equations preserving the same convergence order. Moreover, by adding one more additional step, we obtain minimum 5th-order convergence for every value of a free parameter, θ∈ℝ, and for θ=−1, the method reaches maximum 6-order convergence. We present an extensive convergence analysis of our scheme. The analytical discussion of the work is upheld by performing numerical experiments on some applied science problems and a large system of nonlinear equations. Furthermore, numerical results demonstrate the validity and reliability of the suggested methods