Theory and Modern Applications
Table 1 The temporal errors and convergence orders with \(h=\frac{1}{1000}\)
From: Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation
α | τ | \(e_{\infty}(h,\tau)\) (real part) | \(\mathit{rate1}_{\infty}\) | \(e_{\infty}(h,\tau)\) (Imag. part) | \(\mathit{rate1}_{\infty}\) |
|---|---|---|---|---|---|
0.2 | 1/20 | 4.9502501e − 5 | ∗ | 2.5500257e − 5 | ∗ |
1/40 | 1.5001572e − 5 | 1.72238 | 7.7471511e − 6 | 1.71877 | |
1/80 | 4.5009049e − 6 | 1.73683 | 2.3483707e − 6 | 1.72201 | |
1/160 | 1.3370712e − 6 | 1.75114 | 7.2290069e − 7 | 1.69979 | |
0.4 | 1/20 | 1.7551888e − 4 | ∗ | 8.9455142e − 5 | ∗ |
1/40 | 5.9215472e − 5 | 1.56758 | 3.0178643e − 5 | 1.56756 | |
1/80 | 1.9859482e − 5 | 1.57615 | 1.0137123e − 5 | 1.57594 | |
1/160 | 6.6285477e − 6 | 1.58306 | 3.4053117e − 6 | 1.58237 | |
0.6 | 1/20 | 4.8635429e − 4 | ∗ | 2.4476220e − 4 | ∗ |
1/40 | 1.8560647e − 4 | 1.38976 | 9.3463972e − 5 | 1.38966 | |
1/80 | 7.0665619e − 5 | 1.39317 | 3.5602853e − 5 | 1.39309 | |
1/160 | 2.6857043e − 5 | 1.39570 | 1.3550513e − 5 | 1.39553 | |
0.8 | 1/20 | 1.2232584e − 3 | ∗ | 6.0930267e − 4 | ∗ |
1/40 | 5.3226290e − 4 | 1.20052 | 2.6632309e − 4 | 1.19997 | |
1/80 | 2.3192537e − 4 | 1.19848 | 1.1621693e − 4 | 1.19835 | |
1/160 | 1.0104317e − 4 | 1.19869 | 5.0636302e − 5 | 1.19870 |