A modified hybrid method for solving non-linear equations with computational efficiency

Shehzad Ali Soomro; Asif Ali Shaikh; Sania Qureshi; Bahadur Ali

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A modified hybrid method for solving non-linear equations with computational efficiency

Author(s)

Shehzad Ali Soomro Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Sindh, Pakistan

Asif Ali Shaikh Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Sindh, Pakistan

Sania Qureshi Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology, Jamshoro, Sindh, Pakistan

Bahadur Ali People's University of Medical and Health Sciences for Women Shaheed Benazirabad,Sindh,Pakistan

Abstract

This paper proposes a modified hybrid method for solving nonlinear equations that improves computational efficiency while maintaining accuracy. The proposed method combines the advantages of the traditional Halley's and mean-based methods, resulting in a more efficient algorithm. The modified hybrid method starts with Halley's method and then switches to the mean-based method for rapid convergence. To further improve the efficiency of the algorithm, the proposed method incorporates a dynamic selection criterion to choose the appropriate method at each iteration. Numerical experiments are performed to evaluate the performance of the proposed method in comparison to other existing methods. The results show that the modified hybrid method is computationally efficient and can achieve high accuracy in a shorter time than other commonly used methods having similar features. The proposed method is applicable to a wide range of non-linear equations and can be used in various fields of science and engineering where non-linear equations arise. The modified hybrid method provides an efective tool for solving non-linear equations, ofering significant improvements in computational efficiency over existing methods.

Publication Details

Page(s) 126-137

DOI DOI not available

Published Journal: VFAST Transactions on Mathematics, Volume: 11, Issue: 2, Year: 2023

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Keywords

Convergence, Subject Classification, Efficiency index, Numerical Computations, Newton's method, Processing time, Non-linear equations, Non-linear equations, Non-Linear Equations, Non-Linear Equations, Computational efficiency

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