Abstract
We present iterative methods of convergence order three, five, and six for solving systems of nonlinear equations. Third-order method is composed of two steps, namely, Newton iteration as the first step and weighted-Newton iteration as the second step. Fifth and sixth-order methods are composed of three steps of which the first two steps are same as that of the third-order method whereas the third is again a weighted-Newton step. Computational efficiency in its general form is discussed and a comparison between the efficiencies of proposed techniques with existing ones is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples. It is shown that the present methods have an edge over similar existing methods, particularly when applied to large systems of equations.
Highlights
Solving the system F(x) = 0 of nonlinear equations is a common and important problem in various disciplines of science and engineering [1,2,3,4]
We present iterative methods of convergence order three, five, and six for solving systems of nonlinear equations
To compute F in any iterative method, we evaluate n scalar functions, whereas the number of scalar evaluations is n2 for any new derivative F
Summary
Solving the system F(x) = 0 of nonlinear equations is a common and important problem in various disciplines of science and engineering [1,2,3,4] This problem is precisely stated as follows: For a given nonlinear function F(x) : D ⊆. One of the basic procedures for solving systems of nonlinear equations is the classical Newton’s method [4, 5] which converges quadratically under the conditions that the function F is continuously differentiable and a good initial approximation x(0) is given. It is defined by x(k+1) = G2 (x(k)) = x(k) − F(x(k))−1F (x(k)) , (2). The methods such as those developed in [6,7,8] with second derivative are considered less efficient from a computational point of view
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
