Simpson's rule, was Re: Integrating a Taylor series?
Subject: Simpson's rule, was Re: Integrating a Taylor series?
From: Richard Fateman
Date: Sun, 12 May 2013 15:35:35 -0700
On 5/12/2013 3:25 PM, Richard Fateman wrote:
>
>
> simpson(f,x,a,h) := (h/3)*(f(a)+4*f(a+h)+f(a+2*h));
maybe even better is to put a symbolic coefficient in front of x^4...
that is
ratsimp(
simpson(lambda([x],u*x^4+v*x^3+r*x^2+s*x+t),x,a,h)-integrate(u*x^4+v*x^3+r*x^2+s*x+t,x,a,a+2*h));
which shows you how the error relates to the 4th derivative, 24*u.
The error is (4*h^5/15) * u.