Chapter 4 Numerical Differentiation and Integration
1. Closed Newton-Cotes formulas:
The following denotes the -points closed Newton-Cotes formula with and .
n=1:Trapezoidal rule
,
n=2:Simpson’s rule
,
n=3:Simpson’s three-eighths rule
,
n=4:
.
2. Open Newton-Cotes formulas:
The following denotes the -points open Newton-Cotes formula with and .
n=0:Midpoint rule
,
n=1:
,
n=2:
,
n=3:
References:
【1】
R. L. Burden and J. D. Faires, Numerical Analysis, PWS,