pracma (version 1.8.8)

quadgr: Gaussian Quadrature with Richardson Extrapolation

Description

Gaussian 12-point quadrature with Richardson extrapolation.

Usage

quadgr(f, a, b, tol = .Machine$double.eps^(1/2), ...)

Arguments

f

integrand as function, may have singularities at the endpoints.

a, b

endpoints of the integration interval.

tol

relative tolerence.

...

Additional parameters to be passed to the function f.

Value

• List with value and rel.err.

Details

quadgr uses a 12-point Gauss-Legendre quadrature. The error estimate is based on successive interval bisection. Richardson extrapolation accelerates the convergence for some integrals, especially integrals with endpoint singularities.

Through some preprocessing infinite intervals can also be handled.

See Also

gaussLegendre

Examples

##  Dilogarithm function
flog <- function(t) log(1-t)/t
quadgr(flog, 1, 0, tol = 1e-12)
# value
# 1.6449340668482 , is pi^2/6 = 1.64493406684823
# rel.err
# 2.07167616395054e-13