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A Two-Step Iterative Method for Absolute Value Equations

Alamgir Khan

https://orcid.org/0009-0006-1103-2712

School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, P. R. China

E-mail Address: alamgir.khan@awkum.edu.pk

Corresponding author.

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and

Javed Iqbal

https://orcid.org/0000-0001-7959-0178

Department of Mathematics, Abdul Wali Khan University, Mardan 23200, KPK, Pakistan

E-mail Address: javedmath@gmail.com

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https://doi.org/10.1142/S021987622450018XCited by:0 (Source: Crossref)

Abstract

This paper presents a new numerical iteration method for solving the absolute value equations. The proposed method uses the generalized Newton method as a predictor step, and the five-point open Newton–Cotes formula is considered the corrector step. The convergence of the proposed method is studied in detail. The proposed method solves large systems effectively due to its simplicity and effectiveness. In this paper, we have solved the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solved it using the proposed method. Several numerical examples were provided to demonstrate the accuracy and effectiveness of the new approach. In addition, the novel approach solves absolute value equations with greater accuracy and precision than other existing methods.

Keywords:

AMSC: 65F10, 65H10

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