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Theory and Modern Applications

Table 2 The maximum errors and convergence order in spatial direction with \(\pmb{\tau=10^{-2}}\)

From: Finite difference scheme with spatial fourth-order accuracy for a class of time fractional parabolic equations with variable coefficient

h

α  = 0.9

α  = 0.7

α  = 0.5

e ( Ï„ , h )

\(\boldsymbol {Rate_{h}}\)

e ( Ï„ , h )

\(\boldsymbol {Rate_{h}}\)

e ( Ï„ , h )

\(\boldsymbol {Rate_{h}}\)

\(\frac{ 1}{ 28}\)

7.81649 × 10−5

–

7.84420 × 10−5

–

7.94746 × 10−5

–

\(\frac{ 1}{ 26}\)

1.03531 × 10−4

3.79243

1.05784 × 10−4

4.03520

1.05607 × 10−4

3.83616

\(\frac{ 1}{ 24}\)

1.41482 × 10−4

3.90170

1.43168 × 10−4

3.78067

1.44821 × 10−4

3.94507

\(\frac{ 1}{ 22}\)

2.05058 × 10−4

4.26520

2.01039 × 10−4

3.90157

2.14181 × 10−4

4.49733

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

2.99163 × 10−4

3.96246

3.05069 × 10−4

4.37562

3.13140 × 10−4

3.98520