Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations
Abstract
:1. Introduction
2. Development of the Methods and Convergence Analysis
3. Numerical Examples
- Jaiswal [21] introduced the scheme that achieves optimal convergence order eight as follows:
- , , ,
- , , ,
- , , ,
- , , , .
4. Basins of Attraction
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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NM | JM | ZM | mNH1 | mNH2 | ||
---|---|---|---|---|---|---|
NM | JM | ZM | mNH1 | mNH2 | ||
---|---|---|---|---|---|---|
NM | JM | ZM | mNH1 | mNH2 | ||
---|---|---|---|---|---|---|
0.9851 | 8.0000 | 8.0000 | 8.0000 | 8.0000 | ||
640.0 | 484.0 | 235.0 | 281.0 | 266.0 | ||
0.8999 | 8.0000 | 1.0008 | 8.0000 | 8.0000 | ||
547.0 | 281.0 | 235.0 | 172.0 | 172.0 | ||
6.3(0) | ||||||
1.1281 | 8.0001 | 8.0005 | 8.0000 | 8.0001 | ||
453.0 | 188.0 | 109.0 | 125.0 | 140.0 | ||
1.0111 | 8.0000 | 6.3212 | 8.0000 | 8.0000 | ||
125.0 | 47.0 | 312.0 | 47.0 | 47.0 |
Function | Roots | Multiplicity |
---|---|---|
{} | 2 | |
{ | 2 | |
} | ||
{1.72,1.75,1.75} | 2 | |
2 | ||
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Sariman, S.A.; Hashim, I.; Samat, F.; Alshbool, M. Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations. Mathematics 2021, 9, 1020. https://doi.org/10.3390/math9091020
Sariman SA, Hashim I, Samat F, Alshbool M. Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations. Mathematics. 2021; 9(9):1020. https://doi.org/10.3390/math9091020
Chicago/Turabian StyleSariman, Syahmi Afandi, Ishak Hashim, Faieza Samat, and Mohammed Alshbool. 2021. "Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations" Mathematics 9, no. 9: 1020. https://doi.org/10.3390/math9091020