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Theory and Modern Applications

Table 3 The numerical errors and convergence orders in spatial direction (\(\alpha =0.5\), \(\tau =h^{2}\))

From: An alternating segment Crank–Nicolson parallel difference scheme for the time fractional sub-diffusion equation

M

ID scheme

ASC-N scheme

\(L^{2}_{h,\tau }\)

order 2

CPU (times)

\(L^{2}_{h,\tau }\)

order 2

CPU (times)

20

6.679077e–3

0.083528

9.475760e–3

0.032612

40

1.721474e–3

1.956004

0.121359

2.019811e–3

2.230020

0.040072

80

4.354177e–4

1.983172

1.131083

4.736757e–4

2.092249

0.200203

160

1.094024e–4

1.992754

27.12532

1.142419e–4

2.051806

2.578617

320

2.741480e–5

1.996618

614.8381

2.802388e–5

2.027363

87.60506