Module gauss_quad::legendre

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Expand description

Numerical integration using the Gauss-Legendre quadrature rule.

In Gauss-Legendre quadrature rules the integrand is evaluated at the unique points such that a degree n rule can integrate degree 2n - 1 degree polynomials exactly.

Evaluation point x_i of a degree n rule is the i:th root of Legendre polynomial P_n and its weight is
w = 2 / ((1 - x_i)(P’_n(x_i))^2).

Example

use gauss_quad::legendre::GaussLegendre;
use approx::assert_abs_diff_eq;

let quad = GaussLegendre::init(10);
let integral = quad.integrate(-1.0, 1.0,
    |x| 0.125 * (63.0 * x.powi(5) - 70.0 * x.powi(3) + 15.0 * x)
);
assert_abs_diff_eq!(integral, 0.0);

Structs