A new family of fourth-order Ostrowski-type iterative methods for solving nonlinear systems

Abstract

Ostrowski's iterative method is a classical method for solving systems of nonlinear equations. However, it is not stable enough. In order to obtain a more stable Ostrowski-type method, this paper presented a new family of fourth-order single-parameter Ostrowski-type methods for solving nonlinear systems. As a generalization of the Ostrowski's methods, the Ostrowski's methods are a special case of the new family. It was proved that the order of convergence of the new iterative family was always fourth-order when the parameters take any real number. Finally, the dynamical behavior of the family was briefly analyzed using real dynamical tools. The new iterative method can be applied to solve a wide range of nonlinear equations, and it was used in numerical experiments to solve the Hammerstein equation, boundary value problem, and nonlinear system. These numerical results supported the theoretical results.

Keywords

• nonlinear systems
• iterative method
• stability analysis