newtcotes.m

Integraton routines in matlab

%
% newtcotes.m 
%
% Compute the weights of the Newton-Cotes quadrature quadrature
% on [0,1] with equidistant nodes.
%
%

n = input(' Number n+1 of quadrature nodes n = ');

% nodes 
h = 1/n;
x = (0:h:1)';

% the transpose of the system matrix 
A = ones(n+1,n+1);
for i = 1:n
   A(:,i+1) = A(:,i).*x;
end
% right hand side
d = 1./(1:n+1)';

% Newton-Cotes quadrature weights
w = A'\d;

disp(' Newton-Cotes quadrature weights ')
disp(w')