On a class of efficient higher order Newton-like methods

Abstract

Based on a two-step Newton-like scheme, we propose a three-step scheme of convergence order p+2 (p >=3) for solving systems of nonlinear equations. Furthermore, on the basis of this scheme a generalized k+2-step scheme with increasing convergence order p+2k is presented. Local convergence analysis including radius of convergence and uniqueness results of the methods is presented. Computational efficiency in the general form is discussed. Theoretical results are verified through numerical experimentation. Finally, the performance is demonstrated by the application of the methods on some nonlinear systems of equations.

Keywords

• Newton-like methods
• convergence
• Fr´echet-derivative
• computational efficiency