A New Efficient Method for Absolute Value Equations

Peng Guo, Javed Iqbal (), Syed Muhammad Ghufran, Muhammad Arif, Reem K. Alhefthi and Lei Shi
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Peng Guo: School of Mathematics and Statistics, Anyang Normal University, Anyan 455002, China
Javed Iqbal: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Syed Muhammad Ghufran: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Muhammad Arif: Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Reem K. Alhefthi: College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Lei Shi: School of Mathematics and Statistics, Anyang Normal University, Anyan 455002, China

Mathematics, 2023, vol. 11, issue 15, 1-9

Abstract: In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method’s convergence is discussed in detail. This method is very simple and therefore very effective for solving large systems. In numerical analysis, we consider a beam equation, transform it into a system of absolute value equations and then use the proposed method to solve it. Numerical experiments show that our method is very accurate and faster than already existing methods.

Keywords: absolute value equations; Newton–Cotes open formula; convergence analysis; numerical results; beam equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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