I am looking for references for numerical methods of integration that only use information about the endpoints of integration (like the trapezoidal rule). I have a very unusual problem where I have a continuous function which I can evaluate (and find the derivatives) at the endpoints of integration but not in-between endpoints. Any references to advanced numerical integration methods in one dimension that uses information at the end points would be appreciated.
Notes
- If you need clarification don't hesitate to ask.
- The integral that I am trying to evaluate has been divided into a set of integrals which are much simpler. The endpoints of this simple integrals cannot be changed and the endpoints are not evenly spaced.
- The trapezoidal rule is sufficient for my purposes, but having a more accurate method would be perferable.