Table 2 Numerical simualtion for \({\mathcal {R}}({\omega },{\xi })\) at \(\beta =1\) of Example 4.1.
From: The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature
ine \({\xi }\) | \({\omega }\) | \(|{\mathcal {R}}_{exact}-{\mathcal {R}}^{(4)}|\) | \(|{\mathcal {R}}_{exact}-{\mathcal {R}}^{(5)}|\) | \(|{\mathcal {R}}_{exact}-{\mathcal {R}}^{(6)}|\) |
|---|---|---|---|---|
ine | 0.2 | 3.4807 \(\times \; 10^{-6}\) | 6.93 \(\times \;10^{-8}\) | 1.1 \(\times \;10^{-9}\) |
0.4 | 2.8499 \(\times \; 10^{-6}\) | 5.69 \(\times \; 10^{-8}\) | 1.0 \(\times \; 10^{-9}\) | |
0.1 | 0.6 | 2.3332 \(\times \; 10^{-6}\) | 4.65 \(\times \; 10^{-8}\) | 8.0 \(\times \; 10^{-9}\) |
0.8 | 1.9103 \(\times \; 10^{-6}\) | 3.81 \(\times\; 10^{-8}\) | 7.0 \(\times\; 10^{-9}\) | |
1 | 1.5640 \(\times \; 10^{-6}\) | 3.12 \(\times \; 10^{-8}\) | 5.0 \(\times \; 10^{-9}\) | |
ine | 0.2 | 1.40208 \(\times \; 10^{-4}\) | 6.951 \(\times \; 10^{-6}\) | 2.88 \(\times \; 10^{-7}\) |
0.4 | 1.147924 \(\times \;10^{-4}\) | 5.6908 \(\times\; 10^{-6}\) | 2.357 \(\times \;10^{-7}\) | |
0.25 | 0.6 | 9.39840 \(\times \;10^{-5}\) | 4.6592 \(\times\; 10^{-6}\) | 1.930 \(\times \;10^{-7}\) |
0.8 | 7.69477 \(\times \; 10^{-5}\) | 3.8147 \(\times \; 10^{-6}\) | 1.581 \(\times \; 10^{-7}\) | |
1 | 6.29993 \(\times \; 10^{-5}\) | 3.1231 \(\times \; 10^{-6}\) | 1.293 \(\times \; 10^{-7}\) |
