pracma (version 1.4.5)

romberg: Romberg Integration

Description

Romberg Integration

Usage

romberg(f, a, b, maxit = 50, tol = 1e-6, ...)

Arguments

f

function to be integrated.

a, b

end points of the interval.

maxit

maximum number of iterations.

tol

requested tolerance.

...

variables to be passed to the function.

Value

• List of value, number or iterations, and relative error.

Details

Simple Romberg integration with an explicit Richardson method applied to a series of trapezoidal integrals. This scheme works best with very smmoth functions and needs the least number of function calls among all integration routines.

The function does not need to be vectorized.

References

Chapra, S. C., and R. P. Canale (2006). Numerical Methods for Engineers. Fifth Edition, McGraw-Hill, New York.

See Also

integrate, quadgr

Examples

romberg(sin, 0, pi, tol = 1e-12)    #  2.000000000000001 , rel.error 0
romberg(exp, 0, 1,  tol = 1e-12)    #  1.718281828458432 , rel error 3.6e-13
                                    #  1.718281828459045 , i.e. exp(1) - 1

f <- function(x, p) sin(x) * cos(p*x)
romberg(f, 0, pi, tol = 1e-10, p = 2)   # 2/3
# value: -0.6666667, iter: 6, rel.error: 6.57967e-11