A family of seventh-order schemes for solving nonlinear systems

Abstract

[EN] This paper focuses on solving nonlinear systems numerically. We propose an efficient family of three-step iterative schemes with seventh-order of convergence. The proposed methods are obtained by using the weight functions procedure and they do not require the evaluation of second or higher Frechet derivatives per iteration to proceed. Numerical comparisons are made with other existing methods to confirm the theoretical results and to show the performance of the presented schemes