pracma (version 0.5-3)

romberg: Romberg Integration

Description

Romberg Integration

Usage

romberg(f, a, b, kmax = 16, tol = .Machine$double.eps^(2/3), ...)

Arguments

f

function to be integrated.

a, b

end points of the interval.

kmax

maximum number of iterations

tol

requested tolerance.

...

variables to be passed to the function.

Value

• List of value and absolute error.

Details

Simple Romberg integration with an explicit Richardson method applied to a series of trapezoidal integrals.

References

Mathews, J. H., and K. D. Fink (1999). Numerical Methods Using Matlab. Third Edition, Prentice Hall.

See Also

quadQK15

Examples

romberg(sin, 0, pi)  #  2.000000000000001 , rel.error: 6.6e-13
romberg(exp, 0, 1)   #  1.718281828459044 , rel.error: 3.6e-13
                     #  1.718281828459045 , i.e. exp(1) - 1