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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