A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives
Abstract
1. Introduction
2. Proposed Methods and Their Convergence Analysis
3. Numerical Performance of Proposed Schemes
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Iterations | ||||
---|---|---|---|---|
0.90 | −8.1274e-05+i4.6093e-04 | 9.2186e-04 | 4.6804e-04 | 250 |
0.91 | −3.2556e-05+i2.0787e-04 | 4.1575e-04 | 2.1041e-04 | 250 |
0.92 | −1.0632e-05+i7.7354e-05 | 1.5471e-04 | 7.8081e-05 | 250 |
0.93 | −2.5978e-06+i2.1869e-05 | 4.3739e-05 | 2.2023e-05 | 250 |
0.94 | −4.1185e-07+i4.0939e-06 | 8.1878e-06 | 4.1145e-06 | 250 |
0.95 | −1.6155e-08-i9.1923e-07 | 1.9214e-06 | 9.1937e-07 | 23 |
0.96 | 1.4985e-07-i7.7007e-07 | 1.9468e-06 | 7.8451e-07 | 13 |
0.97 | 3.4521e-07-i7.6249e-07 | 2.6824e-06 | 8.3699e-07 | 9 |
0.98 | 2.7084e-07-i3.4599e-07 | 1.9608e-06 | 4.3939e-07 | 7 |
0.99 | −6.3910e-07+i2.1637e-07 | 6.4318e-06 | 6.7474e-07 | 5 |
1.00 | −2.9769e-08+i0.0000e+00 | 3.0994e-03 | 2.9769e-08 | 3 |
Iterations | ||||
---|---|---|---|---|
0.90 | −8.1270e-05+i4.6090e-04 | 9.2190e-04 | 4.6800e-04 | 250 |
0.91 | −3.2560e-05+i2.0790e-04 | 4.1570e-04 | 2.1040e-04 | 250 |
0.92 | −1.0630e-05+i7.7350e-05 | 1.5470e-04 | 7.8080e-05 | 250 |
0.93 | −2.5980e-06+i2.1870e-05 | 4.3740e-05 | 2.2020e-05 | 250 |
0.94 | −4.1180e-07+i4.0940e-06 | 8.1880e-06 | 4.1150e-06 | 250 |
0.95 | −1.6680e-07+i9.2200e-07 | 1.9640e-06 | 9.3690e-07 | 22 |
0.96 | −3.4850e-07+i7.2840e-07 | 2.0220e-06 | 8.0750e-07 | 12 |
0.97 | 5.5470e-07-i6.3310e-07 | 2.6850e-06 | 8.4180e-07 | 7 |
0.98 | −3.1400e-07+i2.0370e-07 | 1.6820e-06 | 3.7430e-07 | 7 |
0.99 | 1.2990e-07-i8.4600e-08 | 1.2680e-06 | 1.5500e-07 | 6 |
1.00 | −2.9770e-08+i0.0000e+00 | 3.0990e-03 | 2.9770e-08 | 3 |
Iterations | ||||
---|---|---|---|---|
0.90 | −8.1275e-05-i4.6093e-04 | 9.2187e-04 | 4.6804e-04 | 250 |
0.91 | −3.2556e-05-i2.0787e-04 | 4.1575e-04 | 2.1041e-04 | 250 |
0.92 | −1.0632e-05-i7.7354e-05 | 1.5471e-04 | 7.8081e-05 | 250 |
0.93 | −2.5978e-06-i2.1869e-05 | 4.3739e-05 | 2.2023e-05 | 250 |
0.94 | −4.1185e-07+i4.0939e-06 | 8.1878e-06 | 4.1145e-06 | 250 |
0.95 | 2.8656e-08-i9.4754e-07 | 1.9837e-06 | 9.4797e-07 | 23 |
0.96 | −3.2851e-07+i6.6774e-07 | 1.8538e-06 | 7.4418e-07 | 14 |
0.97 | 2.3413e-07-i4.2738e-07 | 1.5022e-06 | 4.8731e-07 | 11 |
0.98 | 2.0677e-07-i2.4623e-07 | 1.4017e-06 | 3.2154e-07 | 9 |
0.99 | 3.0668e-07-i2.2801e-07 | 3.3615e-06 | 3.8216e-07 | 7 |
1.00 | 1.2192e-16+i0.0000e+00 | 3.9356e-06 | 1.2192e-16 | 5 |
Iterations | ||||
---|---|---|---|---|
0.90 | −8.1274e-05-i4.6093e-04 | 9.2186e-04 | 4.6804e-04 | 250 |
0.91 | −3.2556e-05-i2.0787e-04 | 4.1575e-04 | 2.1041e-04 | 250 |
0.92 | −1.0632e-05-i7.7354e-05 | 1.5471e-04 | 7.8081e-05 | 250 |
0.93 | −2.5978e-06-i2.1869e-05 | 4.3739e-05 | 2.2023e-05 | 250 |
0.94 | −4.1185e-07+i4.0939e-06 | 8.1878e-06 | 4.1145e-06 | 250 |
0.95 | −1.1203e-07+i9.8331e-07 | 2.0799e-06 | 9.8967e-07 | 26 |
0.96 | −3.2473e-09-i7.0333e-07 | 1.7375e-06 | 7.0333e-07 | 19 |
0.97 | 5.9619e-08-i7.4110e-07 | 2.3750e-06 | 7.4349e-07 | 18 |
0.98 | 4.7121e-07+i7.4115e-07 | 4.1416e-06 | 8.7826e-07 | 19 |
0.99 | 3.9274e-08-i3.9674e-07 | 3.5758e-06 | 3.9868e-07 | 14 |
1.00 | 3.9559e-08+i4.8445e-07 | 7.8597e-03 | 4.8606e-07 | 8 |
Iterations | ||||
---|---|---|---|---|
0.90 | −8.1308e-05-i4.6100e-04 | 9.2200e-04 | 4.6811e-04 | 250 |
0.91 | −3.2562e-05-i2.0789e-04 | 4.1577e-04 | 2.1042e-04 | 250 |
0.92 | −1.0633e-05-i7.7355e-05 | 1.5471e-04 | 7.8082e-05 | 250 |
0.93 | −2.5978e-06-i2.1870e-05 | 4.3739e-05 | 2.2023e-05 | 250 |
0.94 | −4.1185e-07+i4.0939e-06 | 8.1878e-06 | 4.1145e-06 | 250 |
0.95 | −9.6563e-08+i9.3217e-07 | 1.9628e-06 | 9.3716e-07 | 28 |
0.96 | 1.3446e-08-i7.0728e-07 | 1.7477e-06 | 7.0741e-07 | 22 |
0.97 | −9.7497e-08+i1.0000e+00 | 1.7666e-06 | 2.1081e-07 | 15 |
0.98 | −1.8598e-07-i1.0000e+00 | 5.5924e-06 | 4.4631e-07 | 15 |
0.99 | −1.5051e-07+i5.1262e-07 | 4.9442e-06 | 5.3426e-07 | 13 |
1.00 | 3.9559e-08+i4.8445e-07 | 7.8597e-03 | 4.8606e-07 | 8 |
Iterations | ||||
---|---|---|---|---|
0.90 | −8.1275e-05+i4.6093e-04 | 9.2187e-04 | 4.6804e-04 | 250 |
0.91 | −3.2556e-05+i2.0787e-04 | 4.1575e-04 | 2.1041e-04 | 250 |
0.92 | −1.0632e-05+i7.7354e-05 | 1.5471e-04 | 7.8081e-05 | 250 |
0.93 | −2.5978e-06+i2.1869e-05 | 4.3739e-05 | 2.2023e-05 | 250 |
0.94 | −4.1185e-07+i4.0939e-06 | 8.1878e-06 | 4.1145e-06 | 250 |
0.95 | −9.1749e-08-i9.2392e-07 | 1.9434e-06 | 9.2846e-07 | 28 |
0.96 | 1.5946e-08+i1.0000e+00 | 6.4777e-07 | 1.0272e-07 | 12 |
0.97 | 1.2679e-07+i1.0000e+00 | 4.3336e-06 | 5.1715e-07 | 16 |
0.98 | −5.1142e-07+i7.8442e-07 | 4.5155e-06 | 9.3641e-07 | 16 |
0.99 | 9.3887e-08-i1.0000e+00 | 4.7305e-06 | 1.8942e-07 | 11 |
1.00 | −2.9297e-10-i1.0000e+00 | 1.4107e-05 | 5.9703e-10 | 9 |
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Cordero, A.; Girona, I.; Torregrosa, J.R. A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives. Symmetry 2019, 11, 1017. https://doi.org/10.3390/sym11081017
Cordero A, Girona I, Torregrosa JR. A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives. Symmetry. 2019; 11(8):1017. https://doi.org/10.3390/sym11081017
Chicago/Turabian StyleCordero, Alicia, Ivan Girona, and Juan R. Torregrosa. 2019. "A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives" Symmetry 11, no. 8: 1017. https://doi.org/10.3390/sym11081017
APA StyleCordero, A., Girona, I., & Torregrosa, J. R. (2019). A Variant of Chebyshev’s Method with 3αth-Order of Convergence by Using Fractional Derivatives. Symmetry, 11(8), 1017. https://doi.org/10.3390/sym11081017