Table 8 \(L^{2}\)-norm and convergence rate when \(\beta =0.3, 0.4,0.5\), \(\gamma =0.8,0.7, 0.6\), and \(\tau =h\)

1/2⁴

4.3410e−05

–

4.2505e−05

–

4.2049e−05

–

1/2⁵

1.1659e−05

1.8966

1.1419e−05

1.8962

1.1295e−05

1.8964

1/2⁶

3.0296e−06

1.9442

2.9650e−06

1.9453

2.9310e−06

1.9462

1/2⁷

7.7348e−07

1.9697

7.5638e−07

1.9708

7.4717e−07

1.9719

1/2⁸

1.9606e−07

1.9801

1.9152e−07

1.9816

1.8904e−07

1.9827