Newton-like methods with increasing order of convergence and their convergence analysis in Banach space

Abstract

Based on a two-step Newton-like iterative scheme of convergence order $$p \ge 3$$ , we propose a three-step scheme of convergence order $$p+3$$ . Furthermore, on the basis of this scheme a generalized $$q+2$$ -step scheme with increasing convergence order $$p+3q\,(q \in \mathbb {N})$$ is presented. Local convergence, including radius of convergence and uniqueness results of the methods, is presented. Theoretical results are verified through numerical experimentation. The performance is demonstrated by the application of the methods on some nonlinear systems of equations. The numerical results, including the elapsed CPU-time, confirm the accurate and efficient character of proposed techniques.