First write out Simpson's formula, and then substitute 1 x x^2 x^3 x^4. It is found that the first four are strictly equal, and at the last x^4, the left and right ends of the quadrature formula are no longer equal. We can see that the convergence accuracy h^4 is fourth order, when n\to \infty, h^4 \to 0, so the composite Simpson formula has convergence and stability. This is really: a busy little bee, working hard to pick flowers, spitting out the fragrance of flowers, for whom does it work hard and for whom is it sweet?
All the twists and turns of OJ Simpson's trial of the century from
