An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros
Abstract
:1. Introduction
2. Construction of Higher-Order Scheme
Error for the General form of the Scheme (4)
3. Some Special Cases of Proposed Scheme
- Consider , then we have following new method denoted as
- Consider , then the new method denoted as is obtained as follows:
- Consider , then we have following new method denoted asSimilarly, many more methods can be created by adopting the following weight functions.
- .
- .
4. Numerical Illustration
5. Dynamical Planes of (48) and (49)
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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4.9(−5) | 5.7(−21) | 1.1(−84) | 2.1(−1359) | ||
6.3(−6) | 2.7(−25) | 9.3(−103) | 3.4(−1651) | ||
9.6(−3) | 9.5(−5) | 3.9(−17) | 8.1(−135) | ||
1.1(−3) | 1.7(−14) | 1.1(−57) | 2.3(−922) | ||
6.4(−6) | 2.7(−25) | 9.4(−103) | 3.9(−1651) | ||
5.6(−6) | 1.3(−25) | 4.4(−104) | 9.3(−1673) | ||
5.3(−6) | 9.7(−26) | 1.1(−104) | 2.0(−1682) | ||
5.3(−6) | 9.7(−26) | 1.1(−104) | 1.8(−1682) | ||
4.9(−6) | 6.8(−26) | 2.5(−105) | 4.7(−1693) | ||
5.1(−6) | 8.1(−26) | 5.3(−105) | 1.1(−1687) | ||
5.2(−6) | 8.9(−26) | 7.7(−105) | 4.8(−1685) | ||
4.9(−6) | 6.8(−26) | 2.5(−105) | 4.7(−1693) | ||
5.4(−6) | 1.1(−25) | 2.2(−104) | 1.7(−1677) | ||
5.3(−6) | 9.7(−26) | 1.1(−104) | 1.8(−1682) | ||
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Behl, R.; Bhalla, S.; Magreñán, Á.A.; Moysi, A. An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros. Mathematics 2021, 9, 546. https://doi.org/10.3390/math9050546
Behl R, Bhalla S, Magreñán ÁA, Moysi A. An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros. Mathematics. 2021; 9(5):546. https://doi.org/10.3390/math9050546
Chicago/Turabian StyleBehl, Ramandeep, Sonia Bhalla, Ángel Alberto Magreñán, and Alejandro Moysi. 2021. "An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros" Mathematics 9, no. 5: 546. https://doi.org/10.3390/math9050546
APA StyleBehl, R., Bhalla, S., Magreñán, Á. A., & Moysi, A. (2021). An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros. Mathematics, 9(5), 546. https://doi.org/10.3390/math9050546