# 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** & \(\mathbf{x_{0}}\) & \(\left|\mathbf{x_{k+1}}-\mathbf{x_{k}}\right|\) & \(\left|\mathbf{f(x_{k+1})}\right|\) & **iter** & **ACOC** & **tcpu** \\ \hline \multicolumn{6}{c}{Close to \(\zeta\)} \\ \(f_{1}\) & \(-1.6\) & \(7.6395\times 10^{-19}\) & \(1.8769\times 10^{-110}\) & 3 & 5.5148 & 0.124 \\ \(f_{2}\) & \(-0.4\) & \(1.1915\times 10^{-19}\) & \(3.2336\times 10^{-114}\) & 4 & 6.0717 & 0.2474 \\ \(f_{3}\) & \(0.4\) & \(5.868\times 10^{-64}\) & 0 & 7 & 5.9957 & 0.3128 \\ \(f_{4}\) & \(1.3\) & \(1.2572\times 10^{-32}\) & \(3.2096\times 10^{-195}\) & 3 & 5.717 & 0.7052 \\ \(f_{5}\) & \(-1.9\) & \(2.5535\times 10^{-53}\) & \(6.4242\times 10^{-207}\) & 6 & 5.9132 & 1.3006 \\ \hline \multicolumn{6}{c}{Far from \(\zeta\)} \\ \(f_{1}\) & \(-6\) & \(4.3721\times 10^{-23}\) & \(6.595\times 10^{-136}\) & 4 & 5.7093 & 0.1619 \\ \(f_{2}\) & \(-6\) & \(6.0086\times 10^{-60}\) & 0 & 16 & 5.9975 & 1.0008 \\ \(f_{3}\) & \(-14\) & \(4.2145\times 10^{-24}\) & \(1.1268\times 10^{-140}\) & 10 & 5.8416 & 0.446 \\ \(f_{4}\) & \(-23\) & \(4.6353\times 10^{-98}\) & \(2.3361\times 10^{-207}\) & 5 & 5.9995 & 1.0401 \\ \(f_{5}\) & \(-9\) & \(3.9117\times 10^{-41}\) & \(9.6363\times 10^{-207}\) & 5 & 6.1766 & 1.0393 \\ \hline \multicolumn{6}{c}{Very far from \(\zeta\)} \\ \(f_{1}\) & \(-60\) & \(6.8586\times 10^{-80}\) & 0 & 6 & 5.9981 & 0.2654 \\ \(f_{2}\) & \(-60\) & \(5.9893\times 10^{-27}\) & \(5.2167\times 10^{-158}\) & 6 & 6.0379 & 0.3777 \\ \(f_{3}\) & \(-140\) & \(3.7145\times 10^{-76}\) & 0 & 13 & 5.9983 & 0.5816 \\ \(f_{4}\) & \(-230\) & \(9.2602\times 10^{-68}\) & \(2.3361\times 10^{-207}\) & 6 & 5.9954 & 1.2349 \\ \(f_{5}\) & \(-90\) & \(2.8545\times 10^{-38}\) & \(1.0707\times 10^{-207}\) & 6 & 6.2665 & 1.2801 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical performance of CMT (1) method in nonlinear equations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & \(\mathbf{x_{0}}\) & \(\left|\mathbf{x_{k+1}}-\mathbf{x_{k}}\right|\) & \(\left|\mathbf{f(x_{k+1})}\right|\) & **iter** & **ACOC** & **tcpu** \\ \hline \multicolumn{6}{c}{Close to \(\zeta\)} \\ \(f_{1}\) & \(-1.6\) & \(1.454\times 10^{-49}\) & \(3.8934\times 10^{-208}\) & 4 & 6.0127 & 0.1743 \\ \(f_{2}\) & \(-0.4\) & \(7.7\times 10^{-75}\) & 0 & 40 & 6.006 & 2.5385 \\ \(f_{3}\) & \(0.4\) & nc & nc & nc & nc & nc \\ \(f_{4}\) & \(1.3\) & \(4.1603\times 10^{-29}\) & \(3.3384\times 10^{-172}\) & 3 & 5.3365 & 0.621 \\ \(f_{5}\) & \(-1.9\) & \(1.6341\times 10^{-58}\) & \(2.5794\times 10^{-206}\) & 5 & 5.7418 & 1.1787 \\ \hline \multicolumn{6}{c}{Far from \(\zeta\)} \\ \(f_{1}\) & \(-6\) & nc & nc & nc & nc & nc \\ \(f_{2}\) & \(-6\) & nc & nc & nc & nc & nc \\ \(f_{3}\) & \(-14\) & \(3.9697\times 10^{-26}\) & \(4.0419\times 10^{-151}\) & 7 & 6.0709 & 0.328 \\ \(f_{4}\) & \(-23\) & nc & nc & nc & nc & nc \\ \(f_{5}\) & \(-9\) & \(2.8218\times 10^{-76}\) & \(6.0348\times 10^{-207}\) & 8 & 5.9788 & 1.5886 \\ \hline \multicolumn{6}{c}{Very far from \(\zeta\)} \\ \(f_{1}\) & \(-60\) & \(4.4607\times 10^{-32}\) & \(3.3463\times 10^{-187}\) & 9 & 6.0453 & 0.3717 \\ \(f_{2}\) & \(-60\) & nc & nc & nc & nc & nc \\ \(f_{3}\) & \(-140\) & \(1.7723\times 10^{-57}\) & 0 & 21 & 6.0044 & 0.9822 \\ \(f_{4}\) & \(-230\) & \(1.249\times 10^{-29}\) & \(2.4449\times 10^{-175}\) & 39 & 5.1386 & 7.4938 \\ \(f_{5}\) & \(-90\) & \(6.6349\times 10^{-43}\) & \(4.8668\times 10^{-209}\) & 22 & 6.0131 & 4.4952 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Numerical performance of CMT (\(-300\)) method in nonlinear equations.