Theory and Modern Applications
Table 7 (Example 6.3) \(E_{2}(h,\tau )\), \(E_{\infty }(h,\tau )\) and spatial convergence orders
From: Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation
γ | h | \(E_{2}(h,\tau )\) | Space2 | \(E_{\infty }(h,\tau )\) | \(\text{Space}_{\infty }\) | \(E_{\infty }(h,\tau )\) | \(\text{Space}_{\infty }\) |
|---|---|---|---|---|---|---|---|
Our method | Our method | CNS [36] | |||||
0.1 | 1/5 | 1.6057e−04 | 2.4239e−04 | 3.8406e−04 | |||
1/10 | 8.4508e−07 | 7.5699 | 1.0992e−06 | 7.7847 | 2.3556e−05 | 4.0272 | |
1/20 | 1.0644e−08 | 6.3110 | 1.5054e−08 | 6.1902 | 1.4549e−06 | 4.0171 | |
0.3 | 1/5 | 4.6080e−04 | 6.9537e−04 | 1.1029e−03 | |||
1/10 | 2.4213e−06 | 7.5705 | 3.1527e−06 | 7.7850 | 6.7549e−05 | 4.0292 | |
1/20 | 3.0459e−08 | 6.3128 | 4.3067e−08 | 6.1939 | 4.1711e−06 | 4.0174 | |
0.5 | 1/5 | 7.4202e−04 | 1.1157e−03 | 1.7736e−03 | |||
1/10 | 3.8806e−06 | 7.5790 | 5.0736e−06 | 7.7807 | 1.0865e−04 | 4.0289 | |
1/20 | 5.3287e−08 | 6.1864 | 7.6384e−08 | 6.0536 | 6.6960e−06 | 4.0202 | |