Formulation and convergence analysis of an efficient higher order iterative scheme
Vol 2, Issue 1, 2024
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Abstract
This contribution presents a highly efficient three-step iterative scheme. The proposed scheme is different in itself by achieving seventh-order convergence. The scheme is very useful for equations of nonlinear nature having multiple roots. The Taylor series expansion is employed to rigorously analyze the convergence of the presented scheme. That the scheme is effective and robust can be fit through a variety of examples from different fields. Numerical experimentation demonstrates the scheme’s rapid and reliable convergence to the true root and comparing its performance against existing techniques in the literature. Additionally, basins of attraction are visualized to offer a clear, comparative view of how different methods perform with varying initial guesses. The results show that this new scheme consistently compete well over other methods. This makes it a powerful tool for solving complex equations.
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References
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Copyright (c) 2024 Ranjita Guglani, Ashu Bahl, Rajni Sharma
License URL: https://creativecommons.org/licenses/by/4.0/
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Prof. Youssri Hassan Youssri
Cairo University, Egypt
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