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 | 0.995004 | 0.099833 | 1.025001 | 0.127985 | 1.137524 | 0.124301 |
0.2 | 0.980067 | 0.198669 | 1.013504 | 0.224161 | 1.088189 | 0.143896 |
0.3 | 0.955336 | 0.295520 | 0.982968 | 0.320768 | 1.049366 | 0.279377 |
0.4 | 0.921061 | 0.389418 | 0.945771 | 0.417098 | 1.021368 | 0.361741 |
0.5 | 0.877583 | 0.479426 | 0.900361 | 0.508825 | 0.966005 | 0.448973 |
0.6 | 0.825336 | 0.564642 | 0.845493 | 0.595067 | 0.905687 | 0.534138 |
0.7 | 0.764842 | 0.644218 | 0.782633 | 0.675325 | 0.835528 | 0.610549 |
0.8 | 0.696707 | 0.717356 | 0.709399 | 0.749195 | 0.754661 | 0.681966 |
0.9 | 0.621609 | 0.783327 | 0.628863 | 0.817247 | 0.667961 | 0.746485 |
1 | 0.540302 | 0.841471 | 0.541769 | 0.878423 | 0.572605 | 0.803677 |
RMS | 2.209 × 10−2 | 2.936 × 10−2 | 8.639 × 10−2 | 3.492 × 10−2 | ||
Execution time (second) | 782.9 | 890.2 |