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Theory and Modern Applications

Table 1 The maximum error for Example 1 at different values of h , Δ t for \(\pmb{\gamma=1.5}\) and \(\pmb{t=0.2}\)

From: A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation

h

\(\boldsymbol{\frac{1}{5}}\)

\(\boldsymbol{\frac{1}{10}}\)

\(\boldsymbol{\frac{1}{20}}\)

\(\boldsymbol{\frac{1}{30}}\)

\(\boldsymbol{\frac{1}{30}}\)

\(\boldsymbol{\frac{1}{40}}\)

\(\boldsymbol{\frac{1}{40}}\)

\(\boldsymbol{\frac{1}{45}}\)

Δ t

\(\boldsymbol{\frac{1}{50}}\)

\(\boldsymbol{\frac{1}{100}}\)

\(\boldsymbol{\frac{1}{150}}\)

\(\boldsymbol{\frac{1}{150}}\)

\(\boldsymbol{\frac{1}{200}}\)

\(\boldsymbol{\frac{1}{200}}\)

\(\boldsymbol{\frac{1}{210}}\)

\(\boldsymbol{\frac{1}{220}}\)

HF [14]

0.01149

0.00361

0.00120

0.00115

0.00021

0.00019

0.00006

0.00004

Present method

6.410E − 04

8.203E − 05

1.027E − 05

3.049E − 06

3.035E − 06

1.281E − 06

1.280E − 06

8.989E − 07