Theory and Modern Applications
From: Solving a nonlinear fractional Schrödinger equation using cubic B-splines
t | Exact solution | Numerical solution (CBSM) | Numerical solution (RBFM) | |||
---|---|---|---|---|---|---|
\(p_{1}(t)\) | \(p_{2}(t)\) | \(p^{*}_{1}(t)\) | \(p^{*}_{2}(t)\) | \(p^{*}_{1}(t)\) | \(p^{*}_{2}(t)\) | |
0.1 | 0.000000 | 0.010000 | 0.000111 | 0.009914 | 0.004131 | 0.011617 |
0.2 | 0.000000 | 0.040000 | 0.000470 | 0.040296 | 0.012340 | 0.047792 |
0.3 | 0.000000 | 0.090000 | 0.000963 | 0.091273 | 0.022762 | 0.107879 |
0.4 | 0.000000 | 0.160000 | 0.001525 | 0.162755 | 0.035030 | 0.191759 |
0.5 | 0.000000 | 0.250000 | 0.002211 | 0.254665 | 0.047470 | 0.299435 |
0.6 | 0.000000 | 0.360000 | 0.003083 | 0.367052 | 0.058489 | 0.429440 |
0.7 | 0.000000 | 0.490000 | 0.004163 | 0.500006 | 0.065408 | 0.581127 |
0.8 | 0.000000 | 0.640000 | 0.005487 | 0.653599 | 0.069668 | 0.752353 |
0.9 | 0.000000 | 0.810000 | 0.007167 | 0.827945 | 0.058706 | 0.970170 |
1 | 0.000000 | 1.000000 | 0.009427 | 1.023274 | 0.042043 | 1.206334 |
RMS | 3.969 × 10−3 | 9.692 × 10−3 | 4.700 × 10−2 | 8.62 × 10−2 | ||
Execution time (second) | 710.8 | 833.8 |