A novel families of higher‐order multistep iterative methods for solving nonlinear systems.

In this paper, we propose the first time fifth‐ and sixth‐order two‐step schemes. Based on the proposed two‐step methods, we develop three‐step iterative methods with the ninth‐ and tenth‐order of convergence. We also suggest two parametric families of these schemes. The obtained results are extended to i$$ i $$‐step iterations. The main advantages of the proposed methods are that they are higher order of convergence and utilize only one matrix inversion per iteration which makes these methods computationally more efficient. Numerical experiments are performed to confirm the theoretical results concerning the order of convergence and computational efficiency. [ABSTRACT FROM AUTHOR]