Table 1 Comparison between different methods with errors for Example 3
From: Quadratically convergent algorithm for computing real root of non-linear transcendental equations
Ite no. | BM approx. root | % deviation | R-F approx. root | % deviation | N–R approx. root | % deviation | PM approx. root | % deviation |
|---|---|---|---|---|---|---|---|---|
1 | 0.5000 | – | 0.3147 | – | 1.0000 | – | 0.6573 | – |
2 | 0.7500 | 100 | 0.4467 | 100 | 0.6531 | 100 | 0.4886 | 100 |
3 | 0.6250 | 33.33 | 0.4940 | 29.56 | 0.5313 | 53.12 | 0.5165 | 34.52 |
4 | 0.5625 | 20.00 | 0.5099 | 09.57 | 0.5179 | 22.91 | 0.5176 | 05.40 |
5 | 0.5313 | 11.11 | 0.5152 | 03.12 | 0.5178 | 02.59 | 0.5177 | 00.23 |
6 | 0.5156 | 05.88 | 0.5169 | 01.02 | 0.5178 | 00.03 | 0.5177 | 00.01 |
7 | 0.5234 | 03.03 | 0.5177 | 00.10 | 0.5178 | 00.00 | 0.5178 | 00.00 |
\(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) | ||||
14 | \(\vdots\) | \(\vdots\) | 0.5178 | 00.00 | ||||
\(\vdots\) | \(\vdots\) | \(\vdots\) | ||||||
22 | 0.5178 | 00.00 |