A New High-Order and Efficient Family of Iterative Techniques for Nonlinear Models
Ramandeep Behl, Eulalia Martı́nez
Abstract
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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>θ</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi></mml:mrow></mml:math>, and for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>θ</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>, 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.