Theory and Modern Applications
Table 3 (Example 6.1) Comparing \(E^{\mathrm{Re}}_{\infty }(h,\tau )\) and \(E^{\mathrm{Im}}_{\infty }(h,\tau )\) with other methods
From: Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation
γ | h | \(E^{\text{Re}}_{\infty }(h,\tau )\) | \(E^{\text{Re}}_{\infty }(h,\tau )\) | \(E^{\text{Re}}_{\infty }(h,\tau )\) | \(E^{\text{Im}}_{\infty }(h,\tau )\) | \(E^{\text{Im}}_{\infty }(h,\tau )\) | \(E^{\text{Im}}_{\infty }(h,\tau )\) |
|---|---|---|---|---|---|---|---|
Our method | MC [47] | CNS [36] | Our method | MC [47] | CNS [36] | ||
0.1 | 1/9 | 1.2703e−04 | 7.0404e−02 | 1.2683e−03 | 1.2556e−04 | 7.6325e−02 | 2.4250e−03 |
1/14 | 3.0566e−06 | 2.1873e−02 | 2.2077e−04 | 1.0443e−05 | 2.6090e−02 | 4.1972e−04 | |
1/19 | 4.1062e−07 | 1.0022e−02 | 6.5147e−05 | 1.4591e−06 | 1.2230e−02 | 1.2268e−04 | |
1/24 | 9.4755e−08 | 5.1958e−03 | 2.5400e−05 | 3.2571e−07 | 6.4207e−03 | 4.8343e−05 | |
1/29 | 6.5541e−08 | 2.8536e−03 | 1.1938e−05 | 1.0337e−07 | 3.5662e−03 | 2.2621e−05 | |
0.3 | 1/9 | 1.2838e−04 | 7.0520e−02 | 1.3135e−03 | 1.2426e−04 | 3.5128e−02 | 2.3999e−03 |
1/14 | 3.1059e−06 | 2.1979e−02 | 2.2990e−04 | 1.0361e−05 | 1.4733e−02 | 4.1516e−04 | |
1/19 | 4.0294e−07 | 1.0068e−02 | 6.7510e−05 | 1.5206e−06 | 7.1997e−03 | 1.2140e−04 | |
1/24 | 4.1570e−07 | 5.2146e−03 | 2.6167e−05 | 4.6692e−07 | 3.8478e−03 | 4.7855e−05 | |
1/29 | 4.3146e−07 | 2.8610e−03 | 1.2195e−05 | 2.9081e−07 | 2.1771e−03 | 2.2402e−05 |