Research Article
Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions
Table 1
Numerical results for the fourth-order CFD method in 2D.
| | Scheme I | Scheme II | | Case 1 | Case 2 | Case 1 | Case 2 | | Error | Ratio | Error | Ratio | Error | Ratio | Error | Ratio |
| | 1/4 | 6.613-03 | | 1.279-03 | | 6.613-03 | | 1.270-03 | | | 1/8 | 3.995-04 | 4.04 | 8.355-05 | 3.93 | 3.994-04 | 4.04 | 8.341-05 | 3.92 | | 1/16 | 2.557-05 | 3.96 | 5.273-06 | 3.98 | 2.556-05 | 3.96 | 5.271-06 | 3.98 | | 1/32 | 1.594-06 | 4.00 | 3.330-07 | 3.98 | 1.594-06 | 4.00 | 3.330-07 | 3.98 | | 1/64 | 9.958-08 | 4.00 | 2.082-08 | 3.99 | 9.958-06 | 4.00 | 2.082-08 | 3.99 |
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