◆ qk15()

Finite interval quadrature (15 point Gauss-Kronrod rule)

Purpose: This routine computes
I = integral of f over [a, b] with error estimate, and
J = integral of abs(f) over [a, b],
where f is a given function defined by a user supplied subroutine.
The integral will be evaluated with the 15 point Gauss-Kronrod rule.

Returns: (result, abserr)

result (Float64):
Approximation to I = integral of f over [a, b].

abserr (Float64):
Estimate of the modulus of the absolute error, which should equal or exceed the true error.

Parameters

[in]	f	The user supplied subroutine which calculates the integrand function f(x) defined as follows. _CODE function f(x) returns computed function value f(x). end _ENDCODE
[in]	a	Lower limit of integration.
[in]	b	Upper limit of integration.

Example Program: Compute the following integral.
∫ 1/(1 + x^2) dx [0, 4] (= atan(4))

function TestQk15()

f(x) = 1/(1 + x^2)

a = 0

b = 4

s, abserr = qk15(f, a, b)

println(s, " ", abserr)

end

qk15
function qk15(f::Function, a::Real, b::Real)
Finite interval quadrature (15 point Gauss-Kronrod rule)