Theory and Modern Applications
Table 4 The global errors at different time with \(\pmb{p=0.01}\) and various M , N for Example 6.3
From: An exponential B-spline collocation method for the fractional sub-diffusion equation
M , N | \(\boldsymbol{\|u-u_{N}\|_{L^{2}}}\) | \(\boldsymbol{\|u-u_{N}\|_{L^{\infty}}}\) | ||||
|---|---|---|---|---|---|---|
t = 1 | t = 2 | t = 3 | t = 1 | t = 2 | t = 3 | |
32, 4,000 | 5.4324e-5 | 3.8735e-5 | 3.1716e-5 | 8.8587e-5 | 6.3211e-5 | 5.1768e-5 |
64, 4,000 | 1.3203e-5 | 9.6132e-6 | 7.9258e-6 | 2.1878e-5 | 1.5795e-5 | 1.2985e-5 |
128, 9,000 | 3.0826e-6 | 2.3273e-6 | 1.9418e-6 | 5.2449e-6 | 3.8791e-6 | 3.2140e-6 |
256, 9,000 | 5.3117e-7 | 4.7773e-7 | 4.2641e-7 | 9.5837e-7 | 8.4372e-7 | 7.3492e-7 |
1,024, 250 | 5.9928e-6 | 2.1116e-6 | 1.1412e-6 | 9.4652e-6 | 3.3298e-6 | 1.7970e-6 |
1,024, 500 | 3.6171e-6 | 1.2685e-6 | 6.8189e-7 | 5.6050e-6 | 1.9593e-6 | 1.0500e-6 |
2,048, 1,000 | 2.2589e-6 | 7.9847e-7 | 4.3255e-7 | 3.4336e-6 | 1.2092e-6 | 6.5273e-7 |
2,048, 2,000 | 1.4133e-6 | 4.9781e-7 | 2.6867e-7 | 2.1044e-6 | 7.3642e-7 | 3.9486e-7 |