Table 2 The values of \(p(t)\) for the unperturbed and perturbed model of Example 2
t | 100 | 500 | 1000 | ||||||
|---|---|---|---|---|---|---|---|---|---|
α | \(p_{m}\) | \(p_{a}\) | \(p_{a}^{*}\) | \(p_{m}\) | \(p_{a}\) | \(p_{a}^{*}\) | \(p_{m}\) | \(p_{a}\) | \(p_{a}^{*}\) |
ρ = 0.5 | |||||||||
0.3 | 5.0733 | 5.0741 | 5.0641 | 4.8711 | 4.8705 | 4.8674 | 4.7944 | 4.7939 | 4.7919 |
0.5 | 4.5017 | 4.5004 | 4.4918 | 4.3366 | 4.3360 | 4.3336 | 4.2832 | 4.2828 | 4.2814 |
0.7 | 4.1766 | 4.1759 | 4.1703 | 4.0974 | 4.0972 | 4.0959 | 4.0757 | 4.0756 | 4.0749 |
0.9 | 4.0310 | 4.0310 | 4.0283 | 4.0143 | 4.0143 | 4.0138 | 4.0104 | 4.0104 | 4.0101 |
ρ = 1 | |||||||||
0.3 | 4.7018 | 4.7014 | 4.6994 | 4.4495 | 4.4494 | 4.4490 | 4.3693 | 4.3692 | 4.3690 |
0.5 | 4.2252 | 4.2249 | 4.2230 | 4.1009 | 4.1008 | 4.1005 | 4.0713 | 4.0173 | 4.0712 |
0.7 | 4.0544 | 4.0543 | 4.0526 | 4.0174 | 4.0174 | 4.0170 | 4.0107 | 4.0107 | 4.0105 |
0.9 | 4.0068 | 4.0068 | 4.0051 | 4.0016 | 4.0016 | 4.0012 | 4.0008 | 4.0008 | 4.0007 |
ρ = 1.5 | |||||||||
0.3 | 4.4144 | 4.4143 | 4.4126 | 4.2067 | 4.2067 | 4.2063 | 4.1524 | 4.1524 | 4.1522 |
0.5 | 4.0874 | 4.0873 | 4.0857 | 4.0261 | 4.0261 | 4.0258 | 4.0155 | 4.0155 | 4.0154 |
0.7 | 4.0142 | 4.0142 | 4.0125 | 4.0026 | 4.0026 | 4.0023 | 4.0013 | 4.0013 | 4.0011 |
0.9 | 4.0012 | 4.0012 | 3.9995 | 4.0001 | 4.0001 | 3.9998 | 4.0001 | 4.0001 | 3.9999 |