pracma (version 1.8.8)

cotes: Newton-Cotes Formulas

Description

Closed composite Newton-Cotes formulas of degree 2 to 8.

Usage

cotes(f, a, b, n, nodes, ...)

Arguments

f

the integrand as function of two variables.

a, b

lower and upper limit of the integral.

n

number of subintervals (grid points).

nodes

number of nodes in the Newton-Cotes formula.

...

additional parameters to be passed to the function.

Value

• The integral as a scalar.

Details

2 to 8 point closed and summed Newton-Cotes numerical integration formulas.

These formulas are called `closed' as they include the endpoints. They are called `composite' insofar as they are combined with a Lagrange interpolation over subintervals.

References

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

See Also

simpadpt, trapz

Examples

cotes(sin, 0, pi/2, 20, 2)      # 0.999485905248533
cotes(sin, 0, pi/2, 20, 3)      # 1.000000211546591
cotes(sin, 0, pi/2, 20, 4)      # 1.000000391824184
cotes(sin, 0, pi/2, 20, 5)      # 0.999999999501637
cotes(sin, 0, pi/2, 20, 6)      # 0.999999998927507
cotes(sin, 0, pi/2, 20, 7)      # 1.000000000000363  odd degree is better
cotes(sin, 0, pi/2, 20, 8)      # 1.000000000002231