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Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method

Chein-Shan Liu1, Essam R. El-Zahar2,3, Yung-Wei Chen4,*

1 Center of Excellence for Ocean Engineering, Center of Excellence for the Oceans, National Taiwan Ocean University, Keelung, 202301, Taiwan
2 Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj, 11942, Saudi Arabia
3 Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom, 32511, Egypt
4 Department of Marine Engineering, National Taiwan Ocean University, Keelung, 202301, Taiwan

* Corresponding Author: Yung-Wei Chen. Email: email

Computer Modeling in Engineering & Sciences 2023, 135(2), 1111-1130. https://doi.org/10.32604/cmes.2022.021655

Abstract

How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations (NAEs). This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms. We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system. Through the maximal orthogonal projection concept, to minimize a merit function within a selected interval of splitting parameters, the optimal parameters can be quickly determined. In each step, a linear system is solved by the Gaussian elimination method, and the whole iteration procedure is convergent very fast. Several numerical tests show the high performance of the optimal split-linearization iterative method (OSLIM).

Graphical Abstract

Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method

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APA Style
Liu, C., El-Zahar, E.R., Chen, Y. (2023). Nonlinear algebraic equations solved by an optimal splitting-linearizing iterative method. Computer Modeling in Engineering & Sciences, 135(2), 1111-1130. https://doi.org/10.32604/cmes.2022.021655
Vancouver Style
Liu C, El-Zahar ER, Chen Y. Nonlinear algebraic equations solved by an optimal splitting-linearizing iterative method. Comput Model Eng Sci. 2023;135(2):1111-1130 https://doi.org/10.32604/cmes.2022.021655
IEEE Style
C. Liu, E.R. El-Zahar, and Y. Chen "Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method," Comput. Model. Eng. Sci., vol. 135, no. 2, pp. 1111-1130. 2023. https://doi.org/10.32604/cmes.2022.021655



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