Table 5 The error norms of numerical solutions and the rate of convergence in time where \(h_{x}=h_{y}=0.01\)

DHOC-ADI

0.1

2.13489 × 10⁻²

–

8.43103 × 10⁻²

–

0.05

2.67308 × 10⁻³

2.99758

1.15578 × 10⁻²

2.86684

0.025

6.60480 × 10⁻⁴

2.01692

2.76702 × 10⁻³

2.06247

0.0125

1.64559 × 10⁻⁴

2.00491

6.84316 × 10⁻⁴

2.01560

HOC-ADI

0.1

2.13481 × 10⁻²

–

8.43028 × 10⁻²

–

0.05

2.67269 × 10⁻³

2.99774

1.15540 × 10⁻²

2.86718

0.025

6.60210 × 10⁻⁴

2.01730

2.76494 × 10⁻³

2.06308

0.0125

1.64320 × 10⁻⁴

2.00642

6.81863 × 10⁻⁴

2.01969