Theory and Modern Applications
Table 1 Poincaré-type linear system of difference equations: Numerical results obtained by Algorithm 5.2 and Algorithm 5.3
n | \(W^{(100)}(n)\) | \(\eta ^{(100)}(n)\) |
|---|---|---|
100 | \( \begin{pmatrix} 0&-2.535\cdot 10^{30}\\1.268\cdot 10^{30}&-5.071\cdot 10^{30}\\0&0\\1.268\cdot 10^{30}&1.268\cdot 10^{30}\end{pmatrix}\) | \( \begin{pmatrix} 0&0\\-2.5&1\end{pmatrix}\) |
99 | \( \begin{pmatrix} 4.632\cdot 10^{25}&-1.268\cdot 10^{30}\\ -6.339\cdot 10^{29}&-2.535\cdot 10^{30}\\9.725\cdot 10^{25}&-9.767\cdot 10^{25}\\-6.341\cdot 10^{29}&6.341\cdot 10^{29}\end{pmatrix}\) | \( \begin{pmatrix} -0.0004&0.0002\\ 2.5003&-1.0001\end{pmatrix}\) |
2 | \( \begin{pmatrix} -0.0937&-14.4523\\6.0451&-15.9751\\-1.1255&-9.9137\\8.1103&27.0848\end{pmatrix}\) | \( \begin{pmatrix} -0.8767&0.1726\\3.3005&-1.2905\end{pmatrix}\) |
1 | \( \begin{pmatrix} -0.8344&-3.8417\\-3.1130&-31.8064\\-1.1025&15.9212\\-0.5705&-43.5892\end{pmatrix}\) | \( \begin{pmatrix} -5.8040&1.2016\\8.0617&-2.3442\end{pmatrix}\) |
0 | \( \begin{pmatrix} -0.4438&3.6676\\-4.8386&-3.5192\\2.3796&7.9174\\-6.2876&-8.8716\end{pmatrix}\) | \( \begin{pmatrix} -1.5504&0.6340\\1.0772&-1.3983\end{pmatrix}\) |