|
Newton–Cotes formulas, also called the Newton–Cotes quadrature rules
|
| bet | 3/3 | | Sana | 18.05.2024 | | Hajmi | 75,25 Kb. | | #240927 |
Bog'liq AL MIOpen Newton–Cotes formulas[edit]
This table lists some of the Newton–Cotes formulas of the open type. For , let where , and .
Open Newton–Cotes Formulas
|
n
|
Step size h
|
Common name
|
Formula
|
Error term
|
0
|
|
Rectangle rule, or
midpoint rule
|
|
|
1
|
|
|
|
|
2
|
|
Milne's rule
|
|
|
3
|
|
|
|
|
Composite rules[edit]
For the Newton–Cotes rules to be accurate, the step size h needs to be small, which means that the interval of integration must be small itself, which is not true most of the time. For this reason, one usually performs numerical integration by splitting into smaller subintervals, applying a Newton–Cotes rule on each subinterval, and adding up the results. This is called a composite rule.
|
| |
