# Chaos and Stability in a New Iterative Family for Solving Nonlinear Equations
## 4 Numerical Results
### First Experiment: Efficiency Analysis of CMT (\(\alpha\)) Family
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & \(\mathbf{x_{0}}\) & \(\left|\mathbf{x_{k+1}-x_{k}}\right|\) & \(\left|\mathbf{f(x_{k+1})}\right|\) & **iter** & **ACOC** & **tcpu** \\ \hline \multicolumn{6}{c}{Close to \(\zeta\)} \\ \(f_{1}\) & \(-1.6\) & \(1.8646\times 10^{-19}\) & \(2.7591\times 10^{-114}\) & 3 & 5.5559 & 0.1216 \\ \(f_{2}\) & \(-0.4\) & \(1.3898\times 10^{-46}\) & 0 & 4 & 6.0038 & 0.2775 \\ \(f_{3}\) & \(0.4\) & \(9.0583\times 10^{-50}\) & 0 & 5 & 5.9873 & 0.2321 \\ \(f_{4}\) & \(1.3\) & \(1.9771\times 10^{-32}\) & \(7.3778\times 10^{-194}\) & 3 & 5.6791 & 0.6628 \\ \(f_{5}\) & \(-1.9\) & \(4.057\times 10^{-47}\) & \(1.606\times 10^{-206}\) & 6 & 6.0586 & 1.2462 \\ \hline \multicolumn{6}{c}{Far from \(\zeta\)} \\ \(f_{1}\) & \(-6\) & \(1.4965\times 10^{-24}\) & \(7.3749\times 10^{-145}\) & 4 & 5.7594 & 0.1606 \\ \(f_{2}\) & \(-6\) & \(7.3835\times 10^{-26}\) & \(1.1396\times 10^{-151}\) & 14 & - & 0.8807 \\ \(f_{3}\) & \(-14\) & \(1.009\times 10^{-18}\) & \(1.3833\times 10^{-108}\) & 22 & 5.7241 & 0.9937 \\ \(f_{4}\) & \(-23\) & \(3.2059\times 10^{-100}\) & \(2.3361\times 10^{-207}\) & 5 & 5.9996 & 1.0545 \\ \(f_{5}\) & \(-9\) & \(4.5305\times 10^{-85}\) & \(1.168\times 10^{-207}\) & 7 & 6.0034 & 1.446 \\ \hline \multicolumn{6}{c}{Very far from \(\zeta\)} \\ \(f_{1}\) & \(-60\) & \(1.264\times 10^{-85}\) & 0 & 6 & 5.9988 & 0.2385 \\ \(f_{2}\) & \(-60\) & \(8.3236\times 10^{-19}\) & \(2.3391\times 10^{-109}\) & 9 & 6.0055 & 0.5682 \\ \(f_{3}\) & \(-140\) & \(6.8807\times 10^{-19}\) & \(1.3913\times 10^{-109}\) & 10 & 5.7297 & 0.4723 \\ \(f_{4}\) & \(-230\) & \(1.1069\times 10^{-48}\) & \(2.3361\times 10^{-207}\) & 6 & 6.0195 & 1.2992 \\ \(f_{5}\) & \(-90\) & \(2.3226\times 10^{-65}\) & \(1.168\times 10^{-207}\) & 6 & 5.9808 & 1.3969 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical performance of CMT (\(-1\)) method in nonlinear equations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & \(\mathbf{x_{0}}\) & \(\left|\mathbf{x_{k+1}-x_{k}}\right|\) & \(\left|\mathbf{f(x_{k+1})}\right|\) & **iter** & **ACOC** & **tcpu** \\ \hline \multicolumn{6}{c}{Close to \(\zeta\)} \\ \(f_{1}\) & \(-1.6\) & \(3.9254\times 10^{-19}\) & \(2.9279\times 10^{-112}\) & 3 & 5.5334 & 0.1219 \\ \(f_{2}\) & \(-0.4\) & \(1.0637\times 10^{-28}\) & \(1.328\times 10^{-168}\) & 4 & 6.0263 & 0.2689 \\ \(f_{3}\) & \(0.4\) & \(4.828\times 10^{-30}\) & \(2.1036\times 10^{-176}\) & 6 & 5.9174 & 0.2482 \\ \(f_{4}\) & \(1.3\) & \(1.6112\times 10^{-32}\) & \(1.7919\times 10^{-194}\) & 3 & 5.6961 & 0.6771 \\ \(f_{5}\) & \(-1.9\) & \(3.0345\times 10^{-27}\) & \(1.8831\times 10^{-154}\) & 6 & 6.5022 & 1.2896 \\ \hline \multicolumn{6}{c}{Far from \(\zeta\)} \\ \(f_{1}\) & \(-6\) & \(8.7386\times 10^{-24}\) & \(3.5638\times 10^{-140}\) & 4 & 5.7334 & 0.1602 \\ \(f_{2}\) & \(-6\) & \(6.7903\times 10^{-26}\) & \(8.9867\times 10^{-152}\) & 9 & - & 0.6206 \\ \(f_{3}\) & \(-14\) & \(8.1206\times 10^{-24}\) & \(4.7631\times 10^{-139}\) & 11 & 5.8407 & 0.491 \\ \(f_{4}\) & \(-23\) & \(4.2612\times 10^{-99}\) & \(2.3361\times 10^{-207}\) & 5 & 5.9996 & 1.0585 \\ \(f_{5}\) & \(-9\) & \(4.1362\times 10^{-41}\) & \(2.3361\times 10^{-207}\) & 6 & 5.9265 & 1.2619 \\ \hline \multicolumn{6}{c}{Very far from \(\zeta\)} \\ \(f_{1}\) & \(-60\) & \(1.1445\times 10^{-82}\) & 0 & 6 & 5.9985 & 0.2395 \\ \(f_{2}\) & \(-60\) & \(3.277\times 10^{-54}\) & 0 & 7 & 5.9966 & 0.4971 \\ \(f_{3}\) & \(-140\) & \(3.695\times 10^{-64}\) & 0 & 37 & 5.9959 & 1.6934 \\ \(f_{4}\) & \(-230\) & \(5.2233\times 10^{-59}\) & \(2.3361\times 10^{-207}\) & 6 & 6.0088 & 1.2644 \\ \(f_{5}\) & \(-90\) & \(8.2696\times 10^{-19}\) & \(2.984\times 10^{-103}\) & 6 & 5.5602 & 1.2865 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical performance of CMT (\(0\)) method in nonlinear equations.