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A New Efficient Method for Absolute Value Equations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Peng Guo & Javed Iqbal & Syed Muhammad Ghufran & Muhammad Arif & Reem K. Alhefthi & Lei Shi, 2023. "A New Efficient Method for Absolute Value Equations," Mathematics, MDPI, vol. 11(15), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3356-:d:1207405
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    References listed on IDEAS

    as
    1. Lei Shi & Javed Iqbal & Muhammad Arif & Alamgir Khan, 2020. "A Two-Step Newton-Type Method for Solving System of Absolute Value Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, December.
    2. Muhammad Aslam Noor & Javed Iqbal & Eisa Al-Said, 2012. "Residual Iterative Method for Solving Absolute Value Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, March.
    3. Lei Shi & Javed Iqbal & Faiqa Riaz & Muhammad Arif, 2023. "Gauss Quadrature Method for System of Absolute Value Equations," Mathematics, MDPI, vol. 11(9), pages 1-8, April.
    4. Edalatpour, Vahid & Hezari, Davod & Khojasteh Salkuyeh, Davod, 2017. "A generalization of the Gauss–Seidel iteration method for solving absolute value equations," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 156-167.
    5. Cui-Xia Li, 2016. "A Modified Generalized Newton Method for Absolute Value Equations," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1055-1059, September.
    Full references (including those not matched with items on IDEAS)

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