This paper develops the variants of Chebyshev’s method by applying Lagrange interpolation and finite difference to eliminate the second derivative appearing in the Chebyshev’s method. The results of this research show that the modified eight-order method has the efficiency index 1.5157. Numerical simulations show that the effectiveness and performance of the new method in solving nonlinear equations are encouraging.
| Published in | Applied and Computational Mathematics (Volume 5, Issue 6) |
| DOI | 10.11648/j.acm.20160506.13 |
| Page(s) | 247-251 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Chebyshev’s Method, Finite Differences, Lagrange Interpolation, Nonlinear Equations, Order of Convergence
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APA Style
Muhamad Nizam Muhaijir, M. Imran, Moh Danil Hendry Gamal. (2017). Variants of Chebyshev’s Method with Eighth-Order Convergence for Solving Nonlinear Equations. Applied and Computational Mathematics, 5(6), 247-251. https://doi.org/10.11648/j.acm.20160506.13
ACS Style
Muhamad Nizam Muhaijir; M. Imran; Moh Danil Hendry Gamal. Variants of Chebyshev’s Method with Eighth-Order Convergence for Solving Nonlinear Equations. Appl. Comput. Math. 2017, 5(6), 247-251. doi: 10.11648/j.acm.20160506.13
AMA Style
Muhamad Nizam Muhaijir, M. Imran, Moh Danil Hendry Gamal. Variants of Chebyshev’s Method with Eighth-Order Convergence for Solving Nonlinear Equations. Appl Comput Math. 2017;5(6):247-251. doi: 10.11648/j.acm.20160506.13
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Download@article{10.11648/j.acm.20160506.13,
author = {Muhamad Nizam Muhaijir and M. Imran and Moh Danil Hendry Gamal},
title = {Variants of Chebyshev’s Method with Eighth-Order Convergence for Solving Nonlinear Equations},
journal = {Applied and Computational Mathematics},
volume = {5},
number = {6},
pages = {247-251},
doi = {10.11648/j.acm.20160506.13},
url = {https://doi.org/10.11648/j.acm.20160506.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160506.13},
abstract = {This paper develops the variants of Chebyshev’s method by applying Lagrange interpolation and finite difference to eliminate the second derivative appearing in the Chebyshev’s method. The results of this research show that the modified eight-order method has the efficiency index 1.5157. Numerical simulations show that the effectiveness and performance of the new method in solving nonlinear equations are encouraging.},
year = {2017}
}
TY - JOUR T1 - Variants of Chebyshev’s Method with Eighth-Order Convergence for Solving Nonlinear Equations AU - Muhamad Nizam Muhaijir AU - M. Imran AU - Moh Danil Hendry Gamal Y1 - 2017/02/03 PY - 2017 N1 - https://doi.org/10.11648/j.acm.20160506.13 DO - 10.11648/j.acm.20160506.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 247 EP - 251 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20160506.13 AB - This paper develops the variants of Chebyshev’s method by applying Lagrange interpolation and finite difference to eliminate the second derivative appearing in the Chebyshev’s method. The results of this research show that the modified eight-order method has the efficiency index 1.5157. Numerical simulations show that the effectiveness and performance of the new method in solving nonlinear equations are encouraging. VL - 5 IS - 6 ER -
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