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Theory and Modern Applications

Table 2 A comparison of maximum error \((\Vert \cdot \Vert _{\infty })\) and Euclidean norm \((\Vert \cdot \Vert _{2})\) at \(T=1\) for problem-1

From: A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection–diffusion equation

N

τ = 1.0 × 10−2,γ = 0.5

MCTB-DQM [25]

Proposed method

\(\Vert \cdot \Vert _{\infty }\)

\(\Vert \cdot \Vert _{2}\)

\(\Vert \cdot \Vert _{\infty }\)

\(\Vert \cdot \Vert _{2}\)

Order

CPU time

08

6.3092e−03

4.4047e−03

1.9311e−04

1.4246e−04

0.062400

16

1.6452e−03

1.1394e−03

7.0386e−05

5.1038e−05

1.45609

0.10920

32

4.3121e−04

2.8317e−04

2.6417e−05

1.9079e−05

1.41382

0.23400

64

1.0956e−04

6.4521e−05

5.4923e−06

3.8494e−06

2.26599

0.63960

128

2.7227e−05

1.0443e−05

5.7211e−07

3.0277e−07

3.26304

2.01241