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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