Research Article
A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations
Table 1
Comparison of various third-order methods and Newton’s method.
| | IT | NFE | | Time | |
| | | | | | | NM | 5 | 10 | 0 | 0.062577 | | WF | 3 | 9 | 0 | 0.018731 | | PP | 4 | 12 | 0 | 0.044520 | | CHM | 4 | 12 | 0 | 0.040102 | | HM | 3 | 9 | 0 | 0.019876 | | LM1 | 4 | 12 | 0 | 0.029137 | | LM2 | 3 | 9 | 0 | 0.022242 | | LM3 | 3 | 9 | 0 | 0.023550 | | LM4 | 3 | 9 | 0 | 0.019227 | | LM5 | 3 | 9 | 0 | 0.020131 | | | | | | | | NM | 5 | 10 | 0 | 0.057231 | | WF | 4 | 12 | 0 | 0.039384 | | PP | 4 | 12 | 0 | 0.044239 | | CHM | 4 | 12 | 0 | 0.042782 | | HM | 3 | 9 | 0 | 0.017733 | | LM1 | 4 | 12 | 0 | 0.032638 | | LM2 | 4 | 12 | 0 | 0.037830 | | LM3 | 4 | 12 | 0 | 0.034087 | | LM4 | 4 | 12 | 0 | 0.038399 | | LM5 | 4 | 12 | 0 | 0.035809 | | | | | | | | NM | 4 | 8 | 0 | 0.035702 | | WF | 3 | 9 | 0 | 0.019699 | | PP | 3 | 9 | 0 | 0.021596 | | CHM | 3 | 9 | 0 | 0.023312 | | HM | 3 | 9 | 0 | 0.017431 | | LM1 | 3 | 9 | 0 | 0.016351 | | LM2 | 3 | 9 | 0 | 0.017242 | | LM3 | 3 | 9 | 0 | 0.018978 | | LM4 | 3 | 9 | 0 | 0.016178 | | LM5 | 3 | 9 | 0 | 0.016795 | | | | | | | | NM | 4 | 8 | 0 | 0.044392 | | WF | 3 | 9 | 0 | 0.023132 | | PP | 3 | 9 | 0 | 0.024293 | | CHM | 3 | 9 | 0 | 0.026689 | | HM | 3 | 9 | 0 | 0.022199 | | LM1 | 3 | 9 | 0 | 0.024120 | | LM2 | 3 | 9 | | 0.021035 | | LM3 | 3 | 9 | 0 | 0.021310 | | LM4 | 3 | 9 | 0 | 0.020886 | | LM5 | 3 | 9 | | 0.021592 | | | | | | | | NM | 7 | 14 | | 0.085178 | | WF | 4 | 12 | | 0.030341 | | PP | 5 | 15 | | 0.063971 | | CHM | 5 | 15 | | 0.053064 | | HM | 5 | 15 | | 0.055315 | | LM1 | 5 | 15 | | 0.041370 | | LM2 | 4 | 12 | | 0.026722 | | LM3 | 3 | 9 | | 0.019476 | | LM4 | 4 | 12 | | 0.030513 | | LM5 | 4 | 12 | | 0.031575 | | | | | | | | NM | 6 | 12 | | 0.071738 | | WF | 4 | 12 | | 0.039948 | | PP | 4 | 12 | | 0.056046 | | CHM | 4 | 12 | | 0.036458 | | HM | 4 | 12 | | 0.072238 | | LM1 | 4 | 12 | | 0.033751 | | LM2 | 4 | 12 | | 0.032997 | | LM3 | 4 | 12 | | 0.036425 | | LM4 | 4 | 12 | | 0.034137 | | LM5 | 4 | 12 | | 0.035087 | | | | | | | | NM | 6 | 12 | 0 | 0.071353 | | WF | 4 | 12 | 0 | 0.034140 | | PP | 4 | 12 | 0 | 0.042598 | | CHM | 4 | 12 | 0 | 0.036365 | | HM | 4 | 12 | 0 | 0.038080 | | LM1 | 3 | 9 | 0 | 0.018372 | | LM2 | 4 | 12 | 0 | 0.035562 | | LM3 | 4 | 12 | 0 | 0.036985 | | LM4 | 4 | 12 | 0 | 0.035463 | | LM5 | 4 | 12 | 0 | 0.033362 | | | | | | | | NM | 7 | 14 | 0 | 2.151288 | | WF | 5 | 15 | 0 | 0.054803 | | PP | 5 | 15 | 0 | 0.063380 | | CHM | 5 | 15 | 0 | 0.061753 | | HM | 4 | 12 | 0 | 0.046608 | | LM1 | 5 | 15 | | 0.050909 | | LM2 | 5 | 15 | 0 | 0.048688 | | LM3 | 10 | 30 | 0 | 0.111640 | | LM4 | 4 | 12 | 0 | 0.040109 | | LM5 | 5 | 15 | 0 | 0.043482 | | | | | | | | NM | 5 | 10 | 0 | 0.050123 | | WF | 3 | 9 | 0 | 0.023397 | | PP | 4 | 12 | 0 | 0.038373 | | CHM | 4 | 12 | 0 | 0.037498 | | HM | 4 | 12 | 0 | 0.035701 | | LM1 | 4 | 12 | | 0.028362 | | LM2 | 4 | 12 | 0 | 0.028666 | | LM3 | 6 | 18 | 0 | 0.053924 | | LM4 | 4 | 12 | 0 | 0.028247 | | LM5 | 4 | 12 | 0 | 0.029150 | | | | | | | | NM | 4 | 8 | 0 | 0.039328 | | WF | 2 | 6 | | 0.003092 | | PP | 3 | 9 | 0 | 0.020461 | | CHM | 3 | 9 | 0 | 0.019378 | | HM | 3 | 9 | 0 | 0.018186 | | LM1 | 3 | 9 | 0 | 0.018199 | | LM2 | 3 | 9 | | 0.017732 | | LM3 | 3 | 9 | 0 | 0.013523 | | LM4 | 3 | 9 |
0 | 0.013782 | | LM5 | 3 | 9 | | 0.016581 | | | | | | | | NM | 6 | 12 | | 0.065520 | | WF | 4 | 12 | | 0.030929 | | PP | 16 | 48 | | 0.266014 | | CHM | 5 | 15 | | 0.061006 | | HM | 4 | 12 | | 0.043655 | | LM1 | 4 | 12 | | 0.030877 | | LM2 | 4 | 12 | | 0.031156 | | LM3 | 4 | 12 | | 0.033076 | | LM4 | 5 | 15 | | 0.041102 | | LM5 | 4 | 12 | | 0.030923 | | | | | | | | NM | 6 | 12 | | 0.064979 | | WF | 4 | 12 | | 0.038404 | | PP | 4 | 12 | | 0.042164 | | CHM | 4 | 12 | | 0.043437 | | HM | 4 | 12 | | 0.043896 | | LM1 | 5 | 15 | | 0.053132 | | LM2 | 4 | 12 | | 0.036191 | | LM3 | 6 | 18 | | 0.064485 | | LM4 | 4 | 12 | | 0.035393 | | LM5 | 4 | 12 | | 0.036946 | | | | | | | | NM | 8 | 16 | 0 | 0.114189 | | WF | 6 | 18 | 0 | 0.065645 | | PP | 6 | 18 | 0 | 0.073469 | | CHM | 6 | 18 | 0 | 0.082677 | | HM | 5 | 15 | 0 | 0.055630 | | LM1 | 4 | 12 | 0 | 0.036191 | | LM2 | 5 | 15 | 0 | 0.049599 | | LM3 | 4 | 12 | 0 | 0.038172 | | LM4 | 6 | 18 | 0 | 0.051577 | | LM5 | 5 | 15 | 0 | 0.048340 | | | | | | | | NM | 11 | 22 | 0 | 0.147308 | | WF | 8 | 24 | 0 | 0.106276 | | PP | 8 | 24 | 0 | 0.116999 | | CHM | 7 | 21 | 0 | 0.100725 | | HM | 6 | 18 | 0 | 0.062876 | | LM1 | 6 | 18 | 0 | 0.060920 | | LM2 | 6 | 18 | 0 | 0.060951 | | LM3 | 6 | 18 | 0 | 0.060627 | | LM4 | 7 | 21 | 0 | 0.087873 | | LM5 | 6 | 18 | 0 | 0.060607 | |
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