Research Article
Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations
Table 4
Comparison of the methods for a multiple root.
| | | IT | NOFE | | NMM | HM | OM | ECM | CNM | FAM4 | NMM | HM | OM | ECM | CNM | FAM4 |
| | | 2 | 5 | 3 | 3 | 3 | 3 | 3 | 10 | 9 | 9 | 9 | 9 | 9 | | 1 | 5 | 3 | 4 | 3 | 3 | 3 | 10 | 9 | 12 | 9 | 9 | 9 | | | −0.3 | 54 | 5 | 5 | 5 | 5 | 4 | 108 | 15 | 15 | 15 | 15 | 12 |
| | | 2.3 | 6 | 4 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 12 | 12 | | 2 | 6 | 4 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 12 | 12 | | | 1.5 | 5 | 4 | 4 | 4 | 3 | 3 | 10 | 12 | 12 | 12 | 9 | 9 |
| | | 0 | 4 | 3 | 3 | 3 | 3 | 2 | 8 | 9 | 9 | 9 | 9 | 6 | | 1 | 4 | 4 | 4 | 4 | 4 | 3 | 8 | 12 | 12 | 12 | 12 | 9 | | | | 5 | 4 | 4 | 4 | 4 | 3 | 10 | 12 | 12 | 12 | 12 | 9 |
| | | 1.7 | 5 | 4 | 4 | 4 | 4 | 3 | 10 | 12 | 12 | 12 | 12 | 9 | | 1 | 4 | 3 | 3 | 3 | 3 | 3 | 8 | 9 | 9 | 9 | 9 | 9 | | | −3 | 99 | 8 | 8 | 8 | 8 | 7 | 198 | 24 | 24 | 24 | 24 | 21 |
| | | 3 | 6 | 4 | 5 | 5 | 4 | 4 | 12 | 12 | 15 | 15 | 12 | 12 | | −1 | 10 | 11 | 24 | 23 | 5 | 6 | 20 | 33 | 72 | 79 | 15 | 18 | | | 5 | 8 | 9 | 15 | 15 | 5 | 5 | 16 | 27 | 45 | 45 | 15 | 15 |
| | | | 8 | 5 | 6 | 6 | 6 | 5 | 16 | 15 | 18 | 18 | 18 | 15 | | | 5 | 3 | 4 | 3 | 3 | 5 | 10 | 9 | 12 | 9 | 9 | 15 | | | | 14 | 9 | 10 | 10 | 10 | 9 | 28 | 27 | 30 | 30 | 30 | 27 |
| | | 1.7 | 5 | 3 | 4 | 3 | 4 | 4 | 10 | 9 | 12 | 9 | 12 | 12 | | 2 | 4 | 3 | 3 | 3 | 3 | 3 | 8 | 9 | 9 | 9 | 9 | 9 | | | 3 | 5 | 3 | 3 | 3 | 3 | 3 | 10 | 9 | 9 | 9 | 9 | 9 |
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