Advances in Numerical Analysis

Research Article

A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

Table 2

Experimental error results for Experiment 2.
‖ 𝑢 − 𝑢 ℎ ‖ 𝐿 ∞ HOC4cvge. rate ‖ 𝑢 − 𝑢 ℎ ‖ 𝐿 ∞ HOC 6 1 cvge. rate
1/4 2 . 7 5 0 2 1 8 ⋅ 1 0 − 5 7 . 1 9 0 3 6 2 ⋅ 1 0 − 7
1/8 1 . 7 2 2 5 7 9 ⋅ 1 0 − 6 4.00 1 . 1 2 9 1 2 5 ⋅ 1 0 − 8 5.99
1/16 1 . 1 0 0 9 5 2 ⋅ 1 0 − 7 3.97 1 . 8 0 7 2 3 2 ⋅ 1 0 − 1 0 5.97
1/32 6 . 8 9 3 0 3 2 ⋅ 1 0 − 9 4.00 2 . 8 3 0 7 6 0 ⋅ 1 0 − 1 2 6.00
1/64 4 . 3 1 0 1 3 1 ⋅ 1 0 − 1 0 4.00 4 . 3 5 4 8 5 0 ⋅ 1 0 − 1 4 6.02
HOC 6 2 ( 𝛽 1 9 = 0 . 0 ) rate HOC6 ( 𝛽 7 = 0 . 0 ) rate
1/4 1 . 2 9 9 4 5 3 ⋅ 1 0 − 6 3 . 5 6 9 4 1 0 ⋅ 1 0 − 6
1/8 2 . 3 5 4 9 8 1 ⋅ 1 0 − 8 5.79 6 . 2 8 8 3 6 7 ⋅ 1 0 − 8 5.83
1/16 3 . 6 7 9 9 2 0 ⋅ 1 0 − 1 0 6.00 9 . 8 1 7 2 9 3 ⋅ 1 0 − 1 0 6.00
1/32 5 . 7 7 1 8 4 5 ⋅ 1 0 − 1 2 6.00 1 . 5 4 9 9 5 8 ⋅ 1 0 − 1 1 5.99
1/64 8 . 9 6 7 8 2 6 ⋅ 1 0 − 1 4 6.01 2 . 4 3 1 8 7 4 ⋅ 1 0 − 1 3 5.99
HOC6 ( 𝛽 7 = 𝛽 1 9 ) rate HOC6 ( 𝛽 7 = 2 𝛽 1 9 ) rate
1/4 1 . 9 9 9 1 8 3 ⋅ 1 0 − 6 1 . 2 1 4 0 7 0 ⋅ 1 0 − 6
1/8 3 . 4 0 7 2 5 1 ⋅ 1 0 − 8 5.87 1 . 9 6 6 6 9 3 ⋅ 1 0 − 8 5.95
1/16 5 . 3 7 1 7 1 9 ⋅ 1 0 − 1 0 5.99 3 . 1 8 1 5 4 9 ⋅ 1 0 − 1 0 5.95
1/32 8 . 4 6 9 7 2 5 ⋅ 1 0 − 1 2 5.99 4 . 9 7 1 1 7 6 ⋅ 1 0 − 1 2 6.00
1/64 1 . 3 3 4 9 0 4 ⋅ 1 0 − 1 3 5.99 7 . 8 9 7 8 4 9 ⋅ 1 0 − 1 4 5.98