Theory and Modern Applications
Table 6 The numerical results at \(\pmb{t=1}\) in time with \(\pmb{p=2}\) and \(\pmb{M=2\mbox{,}000}\) for Example 6.5
From: An exponential B-spline collocation method for the fractional sub-diffusion equation
N | \(\boldsymbol{\|u-u_{N}\|_{L^{2}}}\) | Cov. rate | \(\boldsymbol{\|u-u_{N}\|_{L^{\infty}}}\) | Cov. rate | |
|---|---|---|---|---|---|
q = 2 | 5 | 3.5140e-3 | - | 5.1249e-3 | - |
10 | 1.0602e-3 | 1.7288 | 1.5457e-3 | 1.7293 | |
20 | 2.9124e-4 | 1.8641 | 4.2449e-4 | 1.8644 | |
30 | 1.3357e-4 | 1.9224 | 1.9467e-4 | 1.9227 | |
q = 3 | 5 | 1.2790e-3 | - | 1.8610e-3 | - |
10 | 1.9799e-4 | 2.6915 | 2.8777e-4 | 2.6931 | |
20 | 2.7289e-5 | 2.8590 | 3.9643e-5 | 2.8598 | |
30 | 8.3666e-6 | 2.9158 | 1.2150e-5 | 2.9167 | |
q = 4 | 5 | 3.7550e-4 | - | 5.4383e-4 | - |
10 | 2.5907e-5 | 3.8574 | 3.7487e-5 | 3.8587 | |
20 | 1.7273e-6 | 3.9067 | 2.4951e-6 | 3.9092 | |
30 | 3.7751e-7 | 3.7506 | 5.4254e-7 | 3.7631 |