A new efficient two-step iterative method for solving absolute value equations

Abstract

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.

Citation

Khan, A., Iqbal, J. and Shah, R. (2024), "A new efficient two-step iterative method for solving absolute value equations", Engineering Computations, Vol. 41 No. 3, pp. 597-610. https://doi.org/10.1108/EC-11-2023-0781