Research Article
Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions
Table 2
Numerical results for the fourth-order CFD method in 3D.
| | Scheme I | Scheme II | | Case 1 | Case 2 | Case 1 | Case 2 | | Error | Ratio | Error | Ratio | Error | Ratio | Error | Ratio |
| | 1/4 | 1.294-02 | | 4.226-03 | | 1.294-02 | | 4.211-03 | | | 1/8 | 7.523-04 | 4.10 | 2.560-04 | 4.04 | 7.524-04 | 4.10 | 2.558-04 | 4.04 | | 1/16 | 4.740-05 | 3.98 | 1.587-05 | 4.01 | 4.740-05 | 3.98 | 1.587-05 | 4.01 | | 1/32 | 2.954-06 | 4.00 | 9.898-07 | 4.00 | 2.955-06 | 4.00 | 9.898-07 | 4.00 | | 1/64 | 1.849-07 | 3.99 | 6.192-08 | 3.99 | 1.850-07 | 3.99 | 6.192-08 | 3.99 |
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