两个节点复化高斯型求积公式matlab

以下是两个节点复化高斯型求积公式的 MATLAB 代码：

1. 对于区间 [a,b]，使用两个节点的复化高斯型求积公式：

function I = Gauss2(f,a,b)
% Gauss2: 2-node Gauss quadrature
%   I = Gauss2(f,a,b): 2-node Gauss quadrature of f(x) over [a,b]
% input:
%   f = input funtion
%   a,b = integration limits
% output:
%   I = integral of f(x) over [a,b]

x = [-0.5773502692, 0.5773502692];  % nodes
w = [1.0, 1.0];                     % weights
I = (b-a)/2 * sum(w .* f((b-a)/2 * x + (b+a)/2));

2. 对于区间 [a,b]，使用两个节点的复化高斯型求积公式，将区间等分为 n 个子区间，每个子区间使用两个节点的复化高斯型求积公式：

function I = Gauss2c(f,a,b,n)
% Gauss2c: Composite 2-node Gauss quadrature
%   I = Gauss2c(f,a,b,n): Composite 2-node Gauss quadrature of f(x) over [a,b], using n subintervals
% input:
%   f = input funtion
%   a,b = integration limits
%   n = number of subintervals
% output:
%   I = integral of f(x) over [a,b]

x = [-0.5773502692, 0.5773502692];  % nodes
w = [1.0, 1.0];                     % weights
h = (b-a)/n;                        % subinterval width
I = 0;
for i = 1:n
    I = I + sum(w .* f((h/2) * x + (a+(i-0.5)*h)));
end
I = (b-a)/(2*n) * I;