A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots
Abstract
:1. Introduction
2. Construction of Method
3. Main Result
Some Special Cases
4. Numerical Results
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Problems | Root | Multiplicity | Initial Guess |
---|---|---|---|
Isothermal continuous stirred tank reactor problem [25] | |||
−2.85 | 2 | −2.7 | |
Van der Waals problem [26] | |||
1.75 | 2 | 2 | |
Planck law radiation problem [27] | |||
4.9651142317… | 3 | 5.5 | |
Manning problem for isentropic supersonic flow [28] | |||
1.8411294068… | 4 | 1.2 | |
Standard test problem [20] | |||
i | 5 | 1.2i | |
Clustering problem [29] | |||
1 | 20 | 0.7 |
Methods | t | CCO | CPU-Time | |||
---|---|---|---|---|---|---|
SK1 | 4 | 4.000 | 0.0812 | |||
SK2 | 4 | 4.000 | 0.0853 | |||
KM | 4 | 4.000 | 0.0798 | |||
BM | 4 | 4.000 | 0.0788 | |||
NM1 | 4 | 4.000 | 0.0778 | |||
NM2 | 4 | 4.000 | 0.0779 | |||
NM3 | 4 | 4.000 | 0.0784 | |||
NM4 | 4 | 4.000 | 0.0783 | |||
SK1 | 6 | 4.000 | 0.0724 | |||
SK2 | 6 | 4.000 | 0.0942 | |||
KM | 5 | 4.000 | 0.0704 | |||
BM | 5 | 4.000 | 0.0692 | |||
NM1 | 5 | 4.000 | 0.0654 | |||
NM2 | 5 | 4.000 | 0.0472 | |||
NM3 | 5 | 4.000 | 0.0494 | |||
NM4 | 5 | 4.000 | 0.0502 | |||
SK1 | 3 | 0 | 4.000 | 0.4962 | ||
SK2 | 3 | 0 | 4.000 | 0.4726 | ||
KM | 3 | 0 | 4.000 | 0.4137 | ||
BM | 3 | 0 | 4.000 | 0.4232 | ||
NM1 | 3 | 0 | 4.000 | 0.4062 | ||
NM2 | 3 | 0 | 4.000 | 0.4204 | ||
NM3 | 3 | 0 | 4.000 | 0.4247 | ||
NM4 | 3 | 0 | 4.000 | 0.4251 | ||
SK1 | 5 | 4.000 | 3.3120 | |||
SK2 | 5 | 4.000 | 3.2642 | |||
KM | 5 | 4.000 | 3.3230 | |||
BM | 5 | 4.000 | 3.2114 | |||
NM1 | 5 | 4.000 | 3.1423 | |||
NM2 | 5 | 4.000 | 3.1876 | |||
NM3 | 5 | 4.000 | 3.2591 | |||
NM4 | 5 | 4.000 | 2.9642 | |||
SK1 | 4 | 4.000 | 0.5691 | |||
SK2 | 4 | 4.000 | 0.5724 | |||
KM | 4 | 4.000 | 0.5772 | |||
BM | 4 | 4.000 | 0.5547 | |||
NM1 | 4 | 4.000 | 0.5462 | |||
NM2 | 4 | 4.000 | 0.5531 | |||
NM3 | 4 | 4.000 | 0.5684 | |||
NM4 | 4 | 4.000 | 0.5642 | |||
SK1 | 4 | 4.000 | 0.1377 | |||
SK2 | 5 | 4.000 | 0.1421 | |||
KM | 4 | 4.000 | 0.1324 | |||
BM | 4 | 4.000 | 0.1257 | |||
NM1 | 4 | 4.000 | 0.1246 | |||
NM2 | 4 | 4.000 | 0.1098 | |||
NM3 | 4 | 4.000 | 0.1249 | |||
NM4 | 4 | 4.000 | 0.0914 |
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Kumar, S.; Kumar, D.; Sharma, J.R.; Jäntschi, L. A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots. Symmetry 2020, 12, 1969. https://doi.org/10.3390/sym12121969
Kumar S, Kumar D, Sharma JR, Jäntschi L. A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots. Symmetry. 2020; 12(12):1969. https://doi.org/10.3390/sym12121969
Chicago/Turabian StyleKumar, Sunil, Deepak Kumar, Janak Raj Sharma, and Lorentz Jäntschi. 2020. "A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots" Symmetry 12, no. 12: 1969. https://doi.org/10.3390/sym12121969