Research Article
Midpoint Derivative-Based Closed Newton-Cotes Quadrature
Table 3
Computational cost to estimate
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| | Formula | Order | Subintervals | Func. eval | Mid. deriv | Total |
| | Trapezoidal rule | 2 | 462 | 463 | 0 | 463 | | Simpson’s rule | 4 | 8 | 17 | 0 | 17 | | Simpson’s rule | 4 | 7 | 22 | 0 | 22 | | Bool’s rule | 6 | 2 | 9 | 0 | 9 | | Mid. deriv. Trapezoidal rule | 4 | 13 | 14 | 13 | 27 | | Mid. deriv. Simpson’s rule | 6 | 3 | 7 | 3 | 10 | | Mid. deriv. Simpson’s rule | 6 | 3 | 10 | 3 | 13 | | Mid. deriv. Bool’s rule | 8 | 1 | 5 | 1 | 6 |
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