Increased and Extended Convergence of a family of three-step methods

Abstract

In various scientific and engineering disciplines, a wide range of applications can be simplified to the task of solving equations or systems of equations within a carefully selected abstract space. Due to the inherent dificulty or even impossibility of finding analytical solutions, iterative methods are commonly employed to obtain the desired solutions. This article focuses on the presentation of efficient family of three-step iterative methods that exhibit high convergence order. The analysis delves into the local and semi-local convergence properties, considering φ-continuity conditions imposed on the operators utilized. The novel methodology introduced in this article is not limited to specific methods but can be applied to a broader range of approaches that involve the use of inverses of linear operators or matrices.