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A Newton-type technique for solving absolute value equations

The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under mild assumptions. The Newton-type technique i...

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Bibliographic Details
Published in:Alexandria engineering journal 2023-02, Vol.64, p.291-296
Main Authors: Khan, Alamgir, Iqbal, Javed, Akgül, Ali, Ali, Rashid, Du, Yuting, Hussain, Arafat, Nisar, Kottakkaran Sooppy, Vijayakumar, V.
Format: Article
Language:English
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Summary:The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under mild assumptions. The Newton-type technique is very simple and easy to implement. The proposed method is very effective to solve large systems. The heat equation is solved by using the proposed technique. Numerical outcomes show the efficiency of our technique. We add the concluding remarks at the end of this paper.
ISSN:1110-0168
DOI:10.1016/j.aej.2022.08.052