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Theory and Modern Applications

Table 3 Comparison of error norms when \(\gamma =0.9\), \(h=\frac{1}{M}\) for Example 2

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

M

GMMP Scheme [22] (\(\tau =\frac{1}{12}\times 10^{-3}\))

Present Method (τ = 10−3)

 

\(L_{2}\) Norm

\(L_{\infty }\) Norm

\(L_{2}\) Norm

\(L_{\infty }\) Norm

CPU Time (s)

8

4.060e−02

9.248e−02

3.589e−02

4.339e−02

88.66

12

1.803e−02

4.303e−02

1.312e−02

1.935e−02

112.30

16

1.014e−02

2.459e−02

6.387e−03

1.086e−02

146.45

20

6.486e−03

1.585e−02

3.652e−03

6.947e−03

187.38

24

4.502e−03

1.104e−02

2.319e−03

4.831e−03

237.31