Search

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 efciency in the general form is discussed. Theoretical results are verifed through numerical experimentation. Finally, performance is demonstrated by application of the methods on some nonlinear systems of equations. [ABSTRACT FROM AUTHOR]

Numerous higher-order methods with derivative evaluations are accessible in the literature for computing multiple zeros. However, higher-order methods without derivatives are very rare for multiple zeros. Encouraged by this fact, we present a family of third-order derivative-free iterative methods for multiple zeros that require only evaluations of three functions per iteration. Convergence of the proposed class is demonstrated by means of using a graphical tool, namely basins of attraction. Applicability of the methods is demonstrated through numerical experimentation on different functions that illustrates the efficient behavior. Comparison of numerical results shows that the presented iterative methods are good competitors to the existing techniques. [ABSTRACT FROM AUTHOR]

We present a new two-parameter family of fourth-order iterative methods for solving systems of nonlinear equations. The scheme is composed of two Newton–Jarratt steps and requires the evaluation of one function and two first derivatives in each iteration. Convergence including the order of convergence, the radius of convergence, and error bounds is presented. Theoretical results are verified through numerical experimentation. Stability of the proposed class is analyzed and presented by means of using new dynamics tool, namely, the convergence plane. Performance is exhibited by implementing the methods on nonlinear systems of equations, including those resulting from the discretization of the boundary value problem. In addition, numerical comparisons are made with the existing techniques of the same order. Results show the better performance of the proposed techniques than the existing ones. [ABSTRACT FROM AUTHOR]