sll_o_gauss_legendre_integrate_1d Interface Reference

Compute numerical integration with Gauss-Legendre formula. More...

Private Member Functions
real(kind=f64) function	gauss_legendre_integral_1d (f, a, b, n)
	Gauss-Legendre Quadrature. More...

Detailed Description

Compute numerical integration with Gauss-Legendre formula.

Definition at line 61 of file sll_m_gauss_legendre_integration.F90.

Member Function/Subroutine Documentation

gauss_legendre_integral_1d()

real(kind=f64) function gauss_legendre_integral_1d ( procedure(function_1d_legendre)  f, real(kind=f64), intent(in)  a, real(kind=f64), intent(in)  b, integer(kind=i32), intent(in)  n  )

private

Gauss-Legendre Quadrature.

To integrate the function f(x) (real-valued and of a single, real-valued argument x) over the interval [a,b], we use the Gauss-Legendre formula

\[ \int_{-1}^1 f(x)dx \approx \sum_{k=1}^{n} w_k f(x_k) \]

where n represents the desired number of Gauss points.

the function maps the interval [-1,1] into the arbitrary interval [a,b].

To be considered is to split this function into degree-specific functions to avoid the select statement.

Parameters

	f	the function to be integrated
[in]	a	left-bound of the definition interval of f
[in]	b	right-bound of the definition interval of f
[in]	n	the desired number of Gauss points

Returns

The value of the integral

Definition at line 164 of file sll_m_gauss_legendre_integration.F90.

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