Research Article
The Splitting Crank–Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations
Table 4
Comparisons by the maximum errors to Example
1 for
h = 1/19 (i.e.,
K = 3).
| | Methods | r | t = 0.2 | t = 0.4 | t = 0.6 | t = 0.8 |
| | Algorithm 1 | 0.36 | 3.5539e − 4 | 4.8387e − 4 | 5.9795e − 4 | 7.3131e − 4 | | ASC-N scheme [3] | | 4.7468e − 4 | 7.1743e − 4 | 1.0705e − 3 | 1.5969e − 3 | | C-N scheme | | 3.5468e − 4 | 4.7723e − 4 | 5.7998e − 4 | 7.0232e − 4 |
| | Algorithm 1 | 0.72 | 5.7866e − 4 | 7.8813e − 4 | 9.7397e − 4 | 1.1912e − 3 | | ASC-N scheme [3] | | 7.3439e − 4 | 1.1100e − 3 | 1.6563e − 3 | 2.4709e − 3 | | C-N scheme | | 5.7499e − 4 | 7.8239e − 4 | 9.6534e − 4 | 1.0928e − 3 |
| | Algorithm 1 | 1.45 | 1.0066e − 3 | 1.3715e − 3 | 1.6949e − 3 | 2.0729e − 3 | | ASC-N scheme [3] | | 1.0999e − 3 | 1.6591e − 3 | 2.4754e − 3 | 3.6929e − 3 | | C-N scheme | | 9.9823e − 4 | 1.3421e − 3 | 1.6034e − 3 | 1.8807e − 3 |
| | Algorithm 1 | 1.80 | 1.2153e − 3 | 1.6560e − 3 | 2.0465e − 3 | 2.5029e − 3 | | ASC-N scheme [3] | | 1.2843e − 3 | 1.9356e − 3 | 2.8880e − 3 | 4.3084e − 3 | | C-N scheme | | 1.2031e − 3 | 1.6423e − 3 | 1.9034e − 3 | 2.2222e − 3 |
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