Evaluating numerical algorithm
Derived from 5th-degree Newton-Cotes formulas, Weddle's Rule fits 6th-order polynomial stencils across blocks of 7 points (6 subintervals), offering remarkable accuracy when subintervals is a multiple of 6!
Evaluate the classic rational integral:
Using subintervals (multiple of 6)!
With limits and :
| i | x_i | y_i = 1 / (1 + x_i²) | Weddle Weight (w_i) |
|---|---|---|---|
| 0 | 0 | 1.00000 (y_0) | 1 |
| 1 | 1 | 0.50000 (y_1) | 5 |
| 2 | 2 | 0.20000 (y_2) | 1 |
| 3 | 3 | 0.10000 (y_3) | 6 |
| 4 | 4 | 0.05882 (y_4) | 1 |
| 5 | 5 | 0.03846 (y_5) | 5 |
| 6 | 6 | 0.02703 (y_6) | 1 |
Weddle's Rule Formula:
Substituting values:
Using Weddle's 6th-order integration rule with , the calculated value 1.3735 provides exceptional accuracy!