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Purpose: This work presents a new two-step iterative technique for solving absolute value equations. The developed technique is valuable and effective for solving the absolute value equation. Various examples are given to demonstrate the accuracy and efficacy of the suggested technique. Design/methodology/approach: In this paper, we present a new two-step iterative technique for solving absolute value equations. This technique is very straightforward, and due to the simplicity of this approach, it can be used to solve large systems with great effectiveness. Moreover, under certain assumptions, we examine the convergence of the proposed method using various theorems. Numerical outcomes are conducted to present the feasibility of the proposed technique. Findings: This paper gives numerical experiments on how to solve a system of absolute value equations. Originality/value: Nowadays, two-step approaches are very popular for solving equations (1). For solving AVEs, Liu in Shams (2021), Ning and Zhou (2015) demonstrated two-step iterative approaches. Moosaei et al. (2015) introduced a novel approach that utilizes a generalized Newton's approach and Simpson's rule to solve AVEs. Zainali and Lotfi (2018) presented a two-step Newton technique for AVEs that converges linearly. Feng and Liu (2016) have proposed minimization approaches for AVEs and presented their convergence under specific circumstances. Khan et al. (2023), suggested a nonlinear CSCS-like technique and a Picard-CSCS approach. Based on the benefits and drawbacks of the previously mentioned methods, we will provide a two-step iterative approach to efficiently solve equation (1). The numerical results show that our proposed technique converges rapidly and provides a more accurate solution. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]