sll_o_gauss_lobatto_integrate_1d Interface Reference

Integrate numerically with Gauss-Lobatto formula. More...

Private Member Functions
real(kind=f64) function	gauss_lobatto_integral_1d (f, a, b, n)
	Gauss-Lobatto Quadrature. More...

Detailed Description

Integrate numerically with Gauss-Lobatto formula.

Definition at line 38 of file sll_m_gauss_lobatto_integration.F90.

Member Function/Subroutine Documentation

gauss_lobatto_integral_1d()

real(kind=f64) function gauss_lobatto_integral_1d ( procedure(function_1d)  f, real(kind=f64), intent(in)  a, real(kind=f64), intent(in)  b, integer(kind=i32), intent(in)  n  )

private

Gauss-Lobatto 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-Lobatto 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 61 of file sll_m_gauss_lobatto_integration.F90.

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