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Theory and Modern Applications

Table 1 Comparison of error norms when \(\gamma =0.8\), \(h=\frac{\pi }{M}\) for Example 1

From: A collocation method based on cubic trigonometric B-splines for the numerical simulation of the time-fractional diffusion equation

M

GMMP Scheme [22] (\(\tau =\frac{1}{9}\times 10^{-3}\))

Present Method (τ = 10−3)

 

\(L_{2}\) Norm

\(L_{\infty }\) Norm

\(L_{2}\) Norm

\(L_{\infty }\) Norm

CPU Time (s)

4

3.640e−02

5.426e−04

2.105e−02

1.679e−02

43.20

6

1.616e−02

4.331e−02

9.048e−03

7.219e−03

55.55

8

9.075e−03

1.136e−02

5.092e−03

4.063e−03

69.92

10

5.797e−03

7.304e−03

3.301e−03

2.634e−03

87.69

12

4.016e−03

5.080e−03

2.338e−03

1.865e−03

109.06

14

2.942e−03

3.732e−03

1.761e−03

1.405e−03

135.91

16

2.245e−03

2.854e−03

1.387e−03

1.107e−03

155.25

18

1.768e−03

2.252e−03

1.132e−03

9.032e−04

166.62

20

1.426e−03

1.820e−03

9.496e−04

7.577e−04

221.91

22

1.173e−03

1.500e−03

8.149e−04

6.502e−04

223.73

24

9.807e−04

1.257e−03

7.125e−04

5.684e−04

242.34

26

8.310e−04

1.067e−03

6.328e−04

5.049e−04

263.88

28

7.123e−04

9.169e−04

5.697e−04

4.545e−04

298.72

30

6.165e−04

7.955e−04

8.790e−05

4.139e−04

344.34