复合辛普森积分法 Composite Simpson Integration

As \(n\) gets large, Newton-Cotes formulas face Runge's phenomenon, which leads to the drop of precision. Thus in practice, we normally adopt Simpson's Formula, namely the Newton-Cotes formula when \(n=3\). Moreover, to improve precision, we split our target interval into a lot of smaller intervals, apply the formula on each of them and add the integrals up. This is Composite Simpson Integration.
Due to the error restrictions of Simpson's Formula itself, Composite Simpson is more suitable for cases when we have low accuracy goals (say \(10^{-4}\)). For high accuracy goals, we usually adopt Romberg Integration or Gaussian Quadrature.