Does it use the adaptive Simpson quadrature method as used by the quad function when using the default settings?
MATLAB: What algorithm is being used by triplequad
integrationquadtriplequad
Related Solutions
Dear Mariano,
The Mathlab function 'integral(fun,xmin,xmax)' numerically integrates function fun from xmin to xmax using global adaptive quadrature and default error tolerances.
In the documention of this function (doc integral), this ref can be found:
% Portions based on "quadva" by Lawrence F. Shampine.
% Ref: L.F. Shampine, "Vectorized Adaptive Quadrature in Matlab",
% Journal of Computational and Applied Mathematics 211, 2008, pp.131-140
In the Documentation of quadgk you can find a list of multiple quadrature functions that can be used whith there (dis)advantages.
Kind regards, Christiaan
Do you have the symbolic toolbox?
If so, start with the int command. You can do both indefinite and definite integration.
syms x realf = 5 + 1.0./sqrt(1-x^2) % dot-divide not strictly needed here
Q = int(f,x) % indefinite
Q = int(f,x,0,1/2)Now that we have an anlytical answer, 
, we can validate numerical schemes.
, we can validate numerical schemes. First we should make a vectorised anonymous function of the integrand,
f = @(x) 5 + 1.0./sqrt(1-x.^2) Matlab has pre-canned routines for the final two integration schemes:
A3 =quadl(f,0,0.5)A4=integral(f,0,0.5) % Global Adaptive Quadrature
For the (composite) trapz and Simpson's you need to decide on a step size (as you did above).
h = 0.1; % step size (guess)
x=0:h:1/2; A1= trapz(x, f(x))A quick hack of the Simpson's rule is
n = 10; % must be even
a = 0; b = 0.5; % integration limits
x = linspace(a,b,n+1)';c = [1,repmat([4 2],1,n/2-1),4,1];A2 = (b-a)*c*f(x)/n/3; %
It might be prudent to check all numerical values with the analytical one, especially the Simpson's implementation above.
Best Answer