Table 2 Numerical results of Δ and θ for \(\psi _{2}(z)=e^{z}\) and \(\eta \in \mathrm{J} = [0,1]\) in Example 5.1
η | \(\psi _{2}(z)= e^{z}\), \(\rho =\frac{1}{3}\), \(\sigma =\frac{3}{4}\) | ||
|---|---|---|---|
Λ | Δ | \(\theta =0.2\geq \Delta [(\theta +1)^{\ell }-1 +N]\) | |
0.00 | 2.0000 | 0.0902 | 0.2>0.0968 |
0.05 | 1.9609 | 0.0913 | 0.2>0.0979 |
0.10 | 1.9330 | 0.0922 | 0.2>0.0989 |
0.15 | 1.9075 | 0.0930 | 0.2>0.0997 |
0.20 | 1.8829 | 0.1074 | 0.2>0.1177 |
0.25 | 1.8589 | 0.1083 | 0.2>0.1187 |
0.30 | 1.8350 | 0.1093 | 0.2>0.1197 |
0.35 | 1.8111 | 0.1102 | 0.2>0.1208 |
0.40 | 1.7870 | 0.1113 | 0.2>0.1219 |
0.45 | 1.7626 | 0.1124 | 0.2>0.1231 |
0.50 | 1.7378 | 0.1135 | 0.2>0.1243 |
0.55 | 1.7126 | 0.1147 | 0.2>0.1257 |
0.60 | 1.6869 | 0.1160 | 0.2>0.1271 |
0.65 | 1.6605 | 0.1174 | 0.2>0.1286 |
0.70 | 1.6336 | 0.1189 | 0.2>0.1302 |
0.75 | 1.6059 | 0.1204 | 0.2>0.1319 |
0.80 | 1.5775 | 0.1221 | 0.2>0.1338 |
0.85 | 1.5484 | 0.1239 | 0.2>0.1358 |
0.90 | 1.5184 | 0.1259 | 0.2>0.1379 |
0.95 | 1.4875 | 0.1280 | 0.2>0.1402 |
1.00 | 1.4557 | 0.1303 | 0.2>0.1427 |