R: Newton-Cotes Formulas

cotes {pracma} | R Documentation

## 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.

### 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.

### Value

The integral as a scalar.

### Note

It is generally recommended not to apply Newton-Cotes formula of degrees higher than 6, instead increase the number `n` of subintervals used.

### Author(s)

Standard Newton-Cotes formulas can be found in every textbook. Copyright (c) 2005 Greg von Winckel of nicely vectorized Matlab code, available from MatlabCentral, for 2 to 11 grid points. R version by Hans W Borchers, with permission.

### 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

[Package pracma version 2.0.4 Index]