I am studying Gauss Legendre quadrature. I understand the concept and the specifics values that we need to use when applying the formula.
However I am trying to understand if it is possible to integrate a function using the Gauss Legendre method over a certain interval but with a specific step size h,( divided in intervals), as we can do when using another quadrature method.
Basically I am confusing because I cannot find any formula but I read somewhere that if we increase the N ( number of intervals) the result will be more accurate. So is there any Composite Gauss Legendre formula as we have for Composite Simpson method for example?
Thank you
Just split the interval $I = [a,b]$ over which you want to integrate and apply a certain Gauss-Legendre formula over each subinterval. There is no such thing as a closed formula as in the case of Newton-Cotes.